IRANIAN ALGEBRA SEMINAR | Year:2016 | دوره:25 |Papers Count:100

LET R BE A REVERSIBLE RING WHICH IS -COMPATIBLE FOR A DERIVATION ENDOMORPHISM D ON R AND ¦(X) = A0 + A1X +· · ·+ ANXN BE A NON-ZERO POLYNOMIAL IN R[X;D]. IT IS PROVED THAT IF THERE EXISTS A NON-ZERO POLYNOMIAL G(X) = B0+ B1X +· · ·+ BMXM IN R[X;D] SUCH THAT G(X) ¦(X) = C IS A CONSTANT IN R, THEN B0A0=C AND THERE EXIST NON-ZERO ELEMENTS A AND R IN R SUCH THAT R¦(X) =AC. FURTHERMORE, WE SHOW THAT IF B0 IS A UNIT IN R, THEN A1, A2, · · ·, AN ARE ALL NILPOTENT.

LET R BE A COMMUTATIVE RING WITH IDENTITY. FOR A GIVEN CLASS S OF R-MODULES, THE CLASS OF ALL S-PURE FLAT R-MODULES IS COVERING. LET S BE ANY CLASS OF FINITELY PRESENTED R-MODULES CONTAINING R. THEN AN R-MODULE M IS S-PURE FLAT IF AND ONLY IF IT IS A DIRECT LIMIT OF A DIRECT SYSTEM CONSISTING OF R-MODULES ISOMORPHIC TO ELEMENTS BELONG TO ADD (TR(S)).

THE UNDIRECTED POWER GRAPH G(R) OF A RING R IS AN UNDIRECTED GRAPH WHOSE VERTEX SET IS R AND TWO VERTICESA, B Î R ARE ADJACENT IF AND ONLY IF A ¹ B AND AM = B OR BN = A FOR SOME POSITIVE INTEGERS M, N. IN THIS PAPER, WE SHOW THAT IF P IS A PRIME NUMBER, THEN THE POWER GRAPH OF THE DIRECT PRODUCT OF COMMUTATIVE RINGS OF ORDER PN IS THE CARTESIAN PRODUCT OF POWER GRAPHS OF RINGS.

LET (R, M) BE A LOCAL NOETHERIAN RING. WE SHOW THAT COMPLETE MATLIS REFLEXIVE R-MODULE ARE PRECISELY FINITELY GENERATED MODULES.

THE PRESENT PAPER RESTS ON THE CORRESPONDENCE BETWEEN IDEMPOTENT CLOSURE OPERATORS AND THE GENERALIZED NOTION OF RADICALS IN THE CATEGORY OFS -ACTS, S-ACT. THIS CORRESPONDENCE IN THE SEMI-ABELIAN CATEGORIES IS ESTABLISHED AS WELL AS IN THE CATEGORY OFR-MODULES. IN FACT, THE PRESENCE OF A ZERO OBJECT IN A SEMI-ABELIN CATEGORY PROVIDES THE TOOLS NECESSARY FOR PURSUING THE SAME CORRESPONDENCEBETWEEN CLOSURE OPERATORS AND RADICALS. BUT, HERE WE CONSTRUCT THE SAME CORRESPONDENCE IN THE NONSEMI-ABELIAN CATEGORYS-ACT.

LET D BE A DIVISION ALGEBRA FINITE-DIMENSIONAL OVER ITS CENTER F. LET  K1(D) BE ITS WHITEHEAD GROUP AND T(D) BE THE TORSION SUBGROUP OF K1(D). WE ESTABLISH A CONNECTION BETWEEN T(D), DATA OVER THE RESIDUE ALGEBRA, AND RELATIVE VALUE GROUP WHENF ADMITS A HENSELIAN VALUATION. IN THE CASE THAT D IS A NICELY SEMIRAMIFIED DIVISION ALGEBRA WE GIVE AN EXPLICIT FORMULA FOR T(D).

LET J : G ´ X ® X BE A GROUP ACTION ON A COMPACT METRIC SPACE (X, D). IN THIS PAPER, WE INTRODUCE FINITE EXPANSIVE GROUP ACTION, ELASTIC GROUP ACTION AND SHOW THAT NILPOTENT GROUP ACTIONS ONS 1, HAVE NO FINITE EXPANSIVE. ALSO WE SHOW THAT IFH IS FINITE INDEX SUBGROUP OF G, THEN J: G ´ X ® X IS FINITE EXPANSIVE IF AND ONLY IF' J H: H ´ X ® X IS FINITE EXPANSIVE. WE SHOW THAT NILPOTENT GROUP ACTIONS HAVE NO ELASTIC ON A CLOSED INTERVAL BUT THERE IS SOLVABLE GROUP ACTION ON A CLOSED INTERVAL, THAT IS ELASTIC.

LET G=(V(G), E(G)) BE A CONNECTED GRAPH WITH ITS VERTEX SET V(G) = {V1, V2, ..., VN} AND ITS EDGE SET E(G). THE TRANSMISSION TR(VI) OF VERTEX VI IS DEFINED TO BE THE SUM OF THE DISTANCES FROM VI TO ALL OTHER VERTICES. LET TR(G) BE THE N ´ N DIAGONAL MATRIX WITH ITS (I, I) -ENTRY EQUAL TO TRG(VI). THE DISTANCE SIGNLESS LAPLACIAN MATRIX IS DEFINED AS DQ(G) = TR(G) + D(G), WHERE D(G) IS THE DISTANCE MATRIX OF G. THE DISTANCE SIGNLESS LAPLACIAN SPECTRAL RADIUS OF A GRAPH G IS THE LARGEST EIGENVALUE OF DQ(G). IN THIS PAPER WE FIRST DETERMINE SOME UPPER AND LOWER BOUNDS ON THE DISTANCE SIGNLESS LAPLACIAN SPECTRAL RADIUS OF G BASED ON ITS ORDER AND INDEPENDENCE NUMBER, AND CHARACTERIZE THE EXTREMAL GRAPH. IN ADDITION, WE GIVE AN UPPER AND LOWER BOUNDS FOR THE MINIMUM COVERING DISTANCE SIGNLESS LAPLACIAN ENERGY OF G.

LET R BE A RING AND M AN R-MODULE. IN THIS PAPER THE NOTION OF A T-SMALL SUBMODULEIS USED FREQUENTLY. A SUBMODULEN OF M IS T-SMALL IN M (DENOTED BY N <<T&NBSP; M), IF&NBSP; N + K Í Z2 (M) IMPLIES K Í &NBSP;Z2 (M). ALSON IS CALLED T-COCLOSED IN M, IN CASE N/K <<T M/K, FOR A SUBMODULE K CONTAINED IN N, IMPLIES THAT N=K. WE SAY THAT M IS T − D11 IF EVERY T-COCLOSED SUBMODULE OF M HAS A SUPPLEMENT WHICH IS A DIRECT SUMMAND OFM. FOR AN AMPLY SUPPLEMENTED MODULE M, WE PROVE THAT M IS T − D11 IF AND ONLY IF M=Z2 (M) Å&NBSP; L WHERE Z2 (M) AND L ARE BOTH T − D11. SOME RELATIONS OF T − D11-MODULES WITH THE OTHER TYPES OF MODULES INVESTIGATED. EXAMPLES ARE PRESENTED TO SEPARATE DIFFERENT CONCEPTS.

THIS PAPER IS DEVOTED TO THE STUDY OF DIRECT PRODUCTS OF CLASSES OF RIGHTS -POSETS POSSESSING ONE OF THE FLATNESS PROPERTIES AND PRESERVATION OF SUCH PROPERTIES UNDER PRODUCTS. SPECIFICALLY, WE CHARACTERIZE POMONOIDS OVER WHICH THE RIGHTS -POSET SG&NBSP;FOR G&NBSP;¹ F ; SATISFIES FLATNESS PROPERTIES SUCH AS WEAK FLATNESS AND GP- (PO-) FLATNESS.

IN THIS PAPER WE INTRODUCED THE CONCEPT OF COMPLETE ROOTED GRAPHS AND COMPUTE THE HILBERT SERIES OF THEIR BINOMIAL EDGE IDEAL.

LET NC1, ..., CN BE THE VARIETY OF POLYNILPOTENT LIE ALGEBRAS OF CLASS ROW (C1, ..., CN). IN THIS PAPER, WE GENERALIZE, UNDER SOME CONDITIONS, THE GANEA MAP OF GROUPS WITH RESPECT TO THE VARIETY NC1, ..., CN.

THIS PAPER IS DEVOTED TO INTRODUCE THE NOTIONS OF LEFT (RIGHT) HEYTING FILTERS IN RESIDUATED LATTICES AND TO INVESTIGATE THEIR PROPERTIES. SEVERAL CHARACTERIZATIONS OF LEFT (RIGHT) HEYTING FILTERS ARE DERIVED. WE SHOW THAT EACH LEFT (RIGHT) HEYTING FILTER IS A LEFT (RIGHT) NORMAL FILTER AND EACH LEFT AND RIGHT HEYTING FILTER IS A HEYTING FILTER.

IN THIS NOTE A CLASSIFICATION OF ALL CONFIGURATIONS OF LINESZ IN P3 WITH THE WALDSCHMIDT CONSTANT LESS THAN TWO IS GIVEN. WE ALSO, DETERMINE SOME NUMERICAL AND ALGEBRAIC INVARIANTS OF THE IDEAL OF THESE TYPE OF CONFIGURATIONS, FOR EXAMPLE, THE RESURGENCE OF THEIR DEFINING IDEAL I(Z), MINIMAL FREE RESOLUTION OF I(Z), AS WELL AS THE HILBERT FUNCTION OF Z.

A KIND OF MULTIPLICATIVELY CLOSED SUBSET OF C(X) NAMELY ɜ-MCS IS INTRODUCED. RELATING TO EACH ZMCS SUCH AS S, A FILTER FS OF SUBSETS OF X IS PRESENTED AND IT IS SHOWN THAT S −1C (X) AND P(X, FS) ARE ISOMORPHIC RINGS, HERE P(X, FS) IS AN EQUIVALENCE CLASS OF CONTINUOUS REAL-VALUED FUNCTIONS WITH DOMAINS INFS.

IN THIS PAPER, WE INTRODUCE THE CONCEPT OF INTEGRAL IDEALS INBL-ALGEBRAS. WITH RESPECT TO THIS CONCEPT, WE GIVE SOME RELATED RESULTS. IN PARTICULAR, WE PROVE THAT AN INTEGRAL IDEAL IS BOOLEAN AND A PRIME IDEAL. ALSO, WE PROVE THAT ABL-ALGEBRA IS AN INTEGRAL BL-ALGEBRA IF AND ONLY IF THE TRIVIAL IDEAL {0} IS AN INTEGRAL IDEAL. MOREOVER, WE STUDY THE RELATION BETWEEN INTEGRAL IDEALS AND OBSTINATE FILTERS IN BL-ALGEBRAS BY USING THE SET OF THE COMPLEMENTED ELEMENTS.

IN THIS TALK, FIRST WE STATE SOME RELATIONS BETWEEN COLOR VERTEX TRANSITIVITY OF CAY(S,C) AND HCI-ACTS. THEN WE USE THIS RELATION TO CHARACTERIZE COLOR VERTEX TRANSITIVE CAYLEY GRAPHS CAY(S,C), WHEN FOR EVERY S&NBSP;Î S, WE HAVE |ÁCÑS| < ¥.

WE WILL STUDY MODULES WHOSE COFINITE SUBMODULES HAVE GENERALIZED- SUPPLEMENTS. WE ATTEMPT TO INVESTIGATE SOME PROPERTIES OF COFINITELY GENERALIZED-SUPPLEMENTED MODULES. WE WILL PROVE FOR A MODULEM AND A SEMI--HOLLOW SUBMODULE N OF M THAT, M IS COFINITELY GENERALIZED -SUPPLEMENTED IFF M/N IS COFINITELY GENERALIZED-SUPPLEMENTED. ALSO WE WILL PROVE THAT ANY M-GENERATED OF A COFINITELY GENERALIZED-SUPPLEMENTED MODULE M, IS AGAIN COFINITELY GENERALIZED -SUPPLEMENTED. WE WILL GET SOME OTHER SUITABLE RESULTS ABOUT THIS KIND OF MODULES.

IN THIS ARTICLE WE INTRODUCE SOME NEW KINDS OF INJECTIVITIES, NAMELY, LC-INJECTIVITY AND INVESTIGATE THE RELATION AMONG VARIOUS KINDS OF INJECTIVITIES. SOME CLASSIFICATION OF MONOIDS BY PROPERTIES OF THESE KINDS OF INJECTIVE ACTS ARE PRESENTED.

IN THIS TALK, WE FIRST FOCUS ON THE ASSOCIATED PRIMES OF POWERS OF (SQUARE-FREE) MONOMIAL IDEALS IN POLYNOMIAL RINGS. WE NEXT EXTEND THE NOTION OF THE PERSISTENCE PROPERTY FOR MONOMIAL IDEALS TO A FAMILY OF IDEALS IN COMMUTATIVE NOETHERIAN RINGS, AND THEN WE STATE SOME RESULTS IN THIS SUBJECT.

IN THIS PAPER, WE CONSIDER A CLASS OF GRAPHS SATISFYING SOME CONDITIONS ON THE NEIGHBOURHOODS OF THEIR VERTICES. IT IS SHOWN THAT ALL REGULAR SUCH GRAPHS ARE STRONGLY REGULAR GRAPHS. ALSO, IT IS DETERMINED THAT HOW MANY EDGES CAN THESE GRAPHS HAVE?

SUPPOSE THAT SL(X) = {¦&NBSP;Î C (X): |COZ (¦)|=|X \ Z (¦)|< L}, WHERE  IS A REGULAR CARDINAL NUMBER WITH L £ |X|. THE ONE POINT L-COMPACTIFICATION OF A L-DISCRETE SPACE (I.E, EVERY POINT OF X HAS BEEN A NEIGHBORHOOD WITH CARDINAITY IS LESS THAN) IS INTRODUCED AND CHARACTERIZED VIA THE CONCEPT OF THE L-SUPER SOCLE. IN CONTRAST TO THIS FACT THAT CF(X) (I.E, SOCLE OF C (X)) IS NEVER A PRIME IDEAL, IT IS SHOWN THAT SL(X) CAN BE A PRIME IDEAL (EVEN A MAXIMAL IDEAL).

LETR BE AN ASSOCIATIVE RING WITH IDENTITY. IN THIS PAPER WE CHARACTERIZE ZG-REGULAR (RESPECTIVELY, STRONGLY ZG-REGULAR RINGS) AND WE SHOW THAT IN AN ABELIAN ZG-REGULAR RING R, THE NIL (R) IS A TWOSIDED IDEAL OF R AND R&NBSP;/ NIL(R) IS G-REGULAR. FURTHERMORE, THIS PAPER INCLUDES A BRIEF DISCUSSION OF ZG-REGULARITY IN GROUP RINGS.

IN THIS PAPER, USING THE NOTIONS OF DUO AND STRONGLY DUO ACTS, WE GIVE SOME PROPERTIES OF QUASIINJECTIVE ACTS. FOR THE RIGHTS -ACT S S, SEVERAL EQUIVALENT CONDITIONS TO BEING QUASI-INJECTIVE ARE GIVEN. IT IS SHOWN THAT A PROJECTIVE ACT IS STRONGLY DUO IF AND ONLY IF IT IS MULTIPLICATION AND QUASI-INJECTIVE RELATIVE TO ALL INCLUSIONS FROM ITS CYCLIC SUBACTS.

LET S&NBSP;BE ANY RING WITH IDENTITY IN WHICH 2 IS INVERTIBLE AND LET H(S) BE THE QUATERNION RING OVER S. IN THE PRESENT PAPER, WE SHOW THAT ANY JORDAN DERIVATION OF H(S) IS A DERIVATION, AND EVERY DERIVATION OF H(S) DECOMPOSES INTO THE SUM OF A DERIVATION INDUCED BY A DERIVATION ON S AND AN INNER DERIVATION. MOREOVER, WE SHOW THAT EVERY BIDERIVATION OF H(S) IS INNER. SOME RELATED RESULTS ARE ALSO OBTAINED.

FOR AN N-LIE ALGEBRA A OF DIMENSION D, WE FIND THE UPPER BOUND DIM M(A) £ (D N)  , WHERE M(A) DENOTES THE MULTIPLIER OF A, AND THAT THE EQUALITY HOLDS IF AND ONLY IF A IS ABELIAN. FINALLY, WE GIVE A FORMULA FOR DIMENSION OF THE MULTIPLIER OF THE DIRECT SUM OF TWO N-LIE ALGEBRAS.

IN THIS TALK, WE INVESTIGATE WHEN THE IDEAL-BASED ZERO DIVISOR GRAPH IS RING GRAPH, AND ALSO WE STUDY THE CASE THAT IT IS OUTERPLANAR.

LET H= (V, E) BE A HYPERGRAPH, AND FOR A Í V, [A] BE THE INDUCED HYPERGRAPH BY A IN H. IN THIS PAPER, WE SHOW THAT IF THE COLORING COMPLEX OFH IS SHELLABLE, THEN THE COLORING COMPLEX OF [A] IS SHELLABLE, AND HENCE IT IS HOMOTOPY EQUIVALENT TO A WEDGE OF SPHERES, FOR EVERY A Í V.

A RINGR HAS RIGHT PROPERTY (A) IF WHENEVER FINITELY GENERATED TWO-SIDED IDEAL OF R CONSISTING ENTIRELY OF LEFT ZERO-DIVISORS HAS A NON-ZERO RIGHT ANNIHILATOR. AS THE MAIN RESULT OF THIS PAPER WE PROVE THAT IFR IS A RIGHT DUO RING, THEN R[X] AND R[X, X−1] HAVE RIGHT PROPERTY (A).

LET Y BE A SUBSET OF A SPACE X. THEN THE SET OF ALL&NBSP;¦&NBSP;Î C(X) SUCH THAT ¦|Y BE CONSTANT (COUNTABLE) IS A SUBALGEBRA OF C(X), DENOTED BY C1(Y) (CC(Y)) AND Y IS CONSTANT (COUNTABLE) WITH RESPECT TO A SUBRING A OF C(X) IF A Í  C1(Y) (A Í CC (Y)). IF X IS A TOPOLOGICAL SPACE AND Y IS A CONNECTED SUBSET OF X, THEN CC(X) Í&NBSP; C1(Y). IN PARTICULAR, IF &NBSP;X\Y IS COUNTABLE, THEN A  C1(Y) IF AND ONLY IF A Í &NBSP;CC(X). IT IS SHOWN THAT FOR ANY SUBSPACEY OF X, R Í  C1(Y) Í  C(X). MOREOVER, C1(Y) =R IF AND ONLY IF Y IS DENSE INX.

IN THIS TALK, WE STUDY THE ZERO-DIVISOR GRAPH G(P) OF A POSET P. WE CHARACTERIZE ALL POSETS WHOSE G(P) ARE STAR, FINITE COMPLETE BIPARTITE OR FINITE.

IN THIS TALK, AFTER REVIEWING THE CONCEPT OF LOCAL HOMEOMORPHISMS, COVERING MAPS AND FUNDAMENTAL GROUPS, FIRST WE MENTION A RESULT ON UNIQUENESS OF LIFTING FOR LOCAL HOMEOMORPHISM. SECOND, WE PROVE SOME OF THE WELL-KNOWN PROPERTIES OF COVERING MAPS FOR LOCAL HOMEOMORPHISMS WITH UNIQUE PATH LIFTING AND PATH LIFTING PROPERTIES.

ONE OF THE PROBLEMS IN FUZZY GROUP THEORY IS CONCERNED WITH CLASSIFYING THE FUZZY SUBGROUPS OF A FINITE GROUP. IN THIS PAPER, WE USE THE NATURAL EQUIVALENCE RELATION INTRODUCED BY T˘ARN˘AUCEANU AND WE DETERMINE THE NUMBER OF DISTINCT FUZZY SUBGROUPS OF SOME FINITE GROUPS OF ORDER N £ 20.

IN THIS ARTICLE, USING ISOMORPHISMS BETWEEN THE CORRESPONDING TERMS OF THE LOWER CENTRAL SERIES OF THE UPPER CENTRAL QUOTIENTS OF THE LIE ALGEBRAS, WE GIVE ANOTHER EQUIVALENT CONDITION FOR LIE ALGEBRAS TO BEN-ISOCLINIC. ALSO WE OBTAIN SOME RESULTS ON FINITE GENERATED LIE ALGEBRAS ONE CAN BE USE TO.

THE CHARACTER DEGREE GRAPH OF A FINITE GROUP G IS THE GRAPH WHOSE VERTICES ARE THE PRIME DIVISORS OF THE IRREDUCIBLE CHARACTER DEGREES OF G AND TWO VERTICES P AND Q ARE JOINED BY AN EDGE IF PQ DIVIDES SOME IRREDUCIBLE CHARACTER DEGREE OFG. IN THIS TALK WE PROVE THAT THE SIMPLE GROUPS PSL (2, P3) AND PSL (2, P4), WHERE P  11 IS A PRIME NUMBER, ARE UNIQUELY DETERMINED BY THEIR CHARACTER DEGREE GRAPHS AND THEIR ORDERS. LET C1 (G) BE THE SET OF ALL IRREDUCIBLE COMPLEX CHARACTER DEGREES OF G COUNTING MULTIPLICITIES. AS A CONSEQUENCE OF OUR RESULTS WE PROVE THAT IFG IS A FINITE GROUP SUCH THAT C1 (G) =C1 (PSL (2, Q)), WHERE Q=P3 OR Q=P4 AND P ³ 11 IS A PRIME, THEN G @ PSL (2, Q). THIS IMPLIES THAT PSL (2, Q) IS UNIQUELY DETERMINED BY THE STRUCTURE OF ITS COMPLEX GROUP ALGEBRA.

LET CC(X) (RESP. CF(X)) DENOTE THE SUBRING OF C(X) CONSISTING OF FUNCTIONS WITH COUNTABLE (RESP.FINITE) IMAGE AND CF(X) BE THE SOCLE OF C(X). IF X IS ANY TOPOLOGICAL SPACE THERE IS A ZERO-DIMENSIONAL SPACEY SUCH THAT CC(X) @ CC(Y). WE CHARACTERIZE SPACES X WITH C*(X) = CC(X), WHICH GENERALIZES A CELEBRATED RESULT DUE TO RUDIN, PELCZYNNSKI AND SEMADENI. TWO ZERO-DIMENSIONAL COMPACT SPACES X, Y ARE HOMEOMORPHIC IF AND ONLY IF CC(X) @ CC(Y) (RESP. CF(X) @ CF(Y)). THE WELL-KNOWN ALGEBRAIC PROPERTY OF C(X), WHERE X IS REALCOMPACT, IS EXTENDED TO CC(X). IN CONTRAST TO THE FACT THAT CF(X) IS NEVER PRIME IN C(X), WE CHARACTERIZE SPACES X FOR WHICH CF(X) IS A PRIME IDEAL IN CC(X). IT IS OBSERVED FOR THESE SPACES, CC(X) COINCIDES WITH ITS OWN SOCLE (A FACT, WHICH IS NEVER TRUE FOR C(X)). FINALLY, WE SHOW THAT A SPACE X IS THE ONE-POINT COMPACTIFICATION OF A DISCRETE SPACE IF AND ONLY IF CF(X) IS A UNIQUE PROPER ESSENTIAL IDEAL IN CF(X), SEE [9], [10]. A SIMILAR CHARACTERIZATION, AS THE GELFAND-KOLMOGOROFF THEOREM FOR THE MAXIMAL IDEALS IN C(X), IS GIVEN FOR THE MAXIMAL IDEALS OF CC(X), SEE [4]. THE SUBALGEBRA LC(X) = {¦ Í C(X): C¦ = X} OF C(X), WHERE C¦ IS THE UNION OF ALL OPEN SUBSETS U Í &NBSP;X SUCH THAT |¦ (U)| £ À0, WHICH IS CC(X) Í  LC(X)  Í C(X), SEE [13].

IN THIS PAPER, WE INVESTIGATE THE STRUCTURE AND PROPERTIES OF CYCLIC CODES OVER THE RINGS F2+ UF2 WITH U2=U AND F2+ UF2+ U2F2 WITH U3=U. WE FIND A SET OF GENERATORS FOR THESE CODES. EXAMPLES OF CYCLIC CODES OF VARIOUS LENGTHS ALSO STUDIED.

THE RING FP[U] / ÁUKÑ = FP + UFP + U2FP + ... + UK−1 FP MAY BE OF INTEREST IN CODING THEORY, WHICH HAS ALREADY BEEN USED IN OPTIMAL FREQUENCY-HOPPING SEQUENCE. IN THIS PAPER WE PRESENT A DECODING PROCEDURE FOR CYCLIC CODES OVER THE RING FP [U] / ÁUKÑ, WHERE P IS A PRIME NUMBER AND UK=0.

THE POWER GRAPH P(G) OF A FINITE GROUP G IS A GRAPH WHOSE VERTEX SET IS THE GROUP G AND DISTINCT ELEMENTSX, Y Î G ARE ADJACENT IF ONE IS A POWER OF THE OTHER, THAT IS, X AND Y ARE ADJACENT IF X&NBSP;Î&NBSP;(Y) OR Y Î (X). WE CAN FIND GROUPS G WHOSE POWER GRAPHS ARE HAMILTONIAN.

IN THIS NOTE WE STUDY D-SATURATED PROPERTY OF COMPLETELY REGULAR SEMIGROUPS. SINCE COMPLETELY REGULAR SEMIGROUPS ARE SEMILATTICES OF COMPLETELY SIMPLE SEMIGROUPS, FIRST WE CHARACTERIZE CAYLEY GRAPHS OF COMPLETELY SIMPLE SEMIGROUPS AND THE CAYLEY D-SATURATED PROPERTY OF THESE SEMIGROUPS. THEN WE PRESENT THE RELATION BETWEEN THE CAYLEY D-SATURATED PROPERTY OF SEMILATTICE OF SEMIGROUPS AND THE CAYLEY D-SATURATED PROPERTY OF ITS FACTORS.

IN THIS WORK, WE GIVE SOME NECESSARY CONDITIONS FOR 2-CAPABILITY OF GROUPS. MOREOVER, RESULTS DUE TO SHAHRIARI FOR SOME SUBGROUPS OF CAPABLE GROUPS ARE ALSO EXTENDED.

IN THIS PAPER, WE INTRODUCE THE CONCEPT OF FUZZY NIL RADICAL IN A RESIDUATED LATTICE AND OBTAIN SOME BASIC PROPERTIES. WE ALSO PROVE THAT IFΜ IS A FUZZY FILTER (FUZZY BOOLEAN FILTER, FUZZY OBSTINATE FILTER), THE FUZZY NIL RADICAL OF IT, IS ALSO A FUZZY FILTER (RESP. FUZZY BOOLEAN FILTER, FUZZY OBSTINATE FILTER). FURTHERMORE, WE CHARACTERIZE THE FUZZY NIL RADICAL OF A FUZZY FILTER BASED ON ITS LEVEL SUBSETS.

WE INTRODUCE AND STUDY THE CONCEPT OF THE LOCALLY SUPER SOCLE OF C(X), DENOTED BY LS&NBSP;F(X) AS LSF(X) ={ ¦&NBSP;Î&NBSP;C (X): S¦=X O , WHERES F IS THE UNION OF ALL OPEN SUBSETS U IN X SUCH THAT U\Z (¦) IS AS MOST COUNTABLE.LS F(X) IS A Z-IDEAL OF C(X) CONTAINING SCF(X) (I.E., THE SET OF ELEMENTS OF C(X), WHICH ARE ZERO EVERYWHERE EXCEPT ON A COUNTABLE NUMBER OF POINTS OF X). WE CHARACTERIZE SPACES X FOR WHICH THE EQUALITY IN THE RELATION SCF(X)&NBSP;Í  LS F (X) Í &NBSP;C(X) IS HOLD. IN FACT, WE SHOW THAT X IS AN ALMOST COUNTABLE DISCRETE SPACE IF AND ONLY IF LS F(X) = C(X). WE NOTE THAT IF X IS AN INFINITE SPACE, THEN CF(X)&NBSP;Í (C(X). WE ALSO OBSERVE THAT |I(X)| £ À0 IF AND ONLY IF SCF(X) = LS F (X). WE DETERMINE THE CONDITIONS SUCH THAT LS F(X) IS NOT PRIME IN ANY SUBRINGS OF C(X) WHICH CONTAINS THE IDEMPOTENTS OF X. WE INVESTIGATE THE PRIMNESS OF LCF(X) IN SOME SUBRINGS OF C(X).

THE DISTINGUISHING NUMBERD (G) OF A GRAPH G IS THE MINIMUM NUMBER OF COLORS NEEDED TO COLOR THE VERTICES OFG SUCH THAT THE COLORING IS PRESERVED ONLY BY THE TRIVIAL AUTOMORPHISM. IN THIS PAPER WE IMPROVE RESULTS ABOUT THE DISTINGUISHING NUMBER OF CARTESIAN PRODUCTS OF FINITE AND INFINITE GRAPHS BY REMOVING RESTRICTIONS TO PRIME OR RELATIVELY PRIME FACTORS.

LET ¦&NBSP;BE A POSITIVE INTEGER. WE PROVE THAT THERE IS A NUMERICAL SEMIGROUP S WITH EMBEDDING DIMENSION THREE SUCH THAT ¦ IS THE FROBENIUS NUMBER OF S.

LET R BE A RING AND F U {0} THE FREE MONOID GENERATED BY U= {U1, ..., UT} WITH 0 ADDED, AND M A FACTOR OFF SETTING CERTAIN MONOMIAL IN U TO 0, ENOUGH SO THAT, FOR SOME N, MN=0. IN THIS NOTE, WE SHOW THAT THE MONOID RING R[M] IS ARMENDARIZ IF AND ONLY IF R IS REDUCED.

IN THIS PAPER, WE INTRODUCE THE NOTION OF A CONGRUENCE ON AN ULTRA-GROUP OF A SUBGROUP OVER A GIVEN GROUP. FURTHERMORE, WE INVESTIGATE THE CONDITION ON CONGRUENCES ON THE ULTRA-GROUP SUCH THAT THE QUOTIENT ULTRA-GROUP BASED ON IT IS A GROUP.

THIS PAPER IS DEVOTED TO THE PRESERVATION OF INJECTIVE PROPERTIES UNDER LIMITS AND TRANSFERRING THEM FROM COLIMITS TO THEIR COMPONENTS. WE PROVE THAT AN INJECTIVE PROPERTY A&NBSP;IS PRESERVED UNDER LIMITS IF AND ONLY IF ALL ACTS SATISFY PROPERTY A. BESIDES WE PROVE THAT AN INJECTIVE PROPERTY A&NBSP;TRANSFERRED FROM COLIMITS TO THEIR COMPONENTS IF AND ONLY IF ALL ACTS SATISFY PROPERTY A.

LET D(G) AND G2(G) BE THE MINIMAL NUMBER OF GENERATORS OF G AND THE SECOND TERM OF LOWER CENTRAL SERIES OF G, RESPECTIVELY. IN THIS TALK, SOME PROPERTIES OF P-GROUPS IN C ARE GIVEN, IN WHICH C &NBSP;IS THE SET OF ALL GROUPSG SUCH THAT |G/Z (G)|=|G2 (G)|D(G/Z (G)).

ONE OF THE MOST IMPORTANT TOOLS IN ALGEBRAIC (M, N) -HYPERSTRUCTURES IS REPRESENTED BY STRONGLY REGULAR RELATIONS, WHICH CONNECTS AN ALGEBRAIC (M, N) -HYPERSTRUCTURE TO THE ASSOCIATED ALGEBRAIC (M, N) -STRUCTURE. IN THIS PAPER, WE DEFINE THE NOTION OF A NORMAL HYPERIDEAL FOR A KRASNER (M, N) -HYPERRING AND SHOW THAT IT HAS A BEHAVIOR SIMILAR TO STRONGLY REGULAR RELATIONS AND WE CAN OBTAIN TRIVIAL KRASNER (M, N) -HYPERRINGS BY IT.

THERE ARE SOME GRAPHS RELATED TO THE STRUCTURE OF A FINITE GROUP, SAY PRIME GRAPH, SOLVABLE GRAPH, AND NON-COMMUTING GRAPH OF A FINITE GROUP. IN THIS PAPER, WE CONSIDER THE CHARACTERIZATION BY ORDER AND PRIME GRAPH OF ALTERNATING GROUPS. IN PARTICULAR, WE SHOW THAT THERE EXISTS A CLOSED RELATION BETWEEN THE CHARACTERIZATION BY ORDER AND PRIME GRAPH OF SOME OF ALTERNATING GROUPS AND GOLDBACH’S CONJECTURE.

LET (K, V) BE A HENSELIAN VALUED FIELD OF ARBITRARY RANK. A FINITE EXTENSION (K', V') OF (K, V) IS SAID TO BE DEFECTLESS IF [K': K] =E F, WHERE E AND F ARE, RESPECTIVELY, THE RAMIFICATION INDEX AND THE RESIDUAL DEGREE OF (K', V') / (K, V). DEFECTLESS EXTENSIONS HAVE BEEN EXTENSIVELY USED TO SOLVE MANY PROBLEMS IN VALUATION THEORY. IN THIS PAPER, WE EMPLOY THE NOTION OF COMPLETE DISTINGUISHED CHAINS TO GIVE A DIFFERENT CHARACTERIZATION OF DEFECTLESS EXTENSIONS OF A HENSELIAN VALUED FIELD.

WE PRESENT A NEW ALGORITHM FOR COMPUTING A SAGBI BASIS UP TO AN ARBITRARY DEGREET FOR A SUBALGEBRA GENERATED BY A SET OF HOMOGENEOUS POLYNOMIALS. OUR IDEA IS BASED ON LINEAR ALGEBRA METHODS WHICH CAUSE A LOW LEVEL OF COMPLEXITY AND COMPUTATIONAL COST. WE THEN USE IT TO SOLVE THE MEMBERSHIP PROBLEM IN SUBALGEBRAS.

IN THIS ARTICLE, WE DEFINE AND INVESTIGATE 2-ABSORBING SUBACTS AND STRONGLY 2-ABSORBING SUBACTS OF S-ACTS OVER MONOIDS WITH UNIQUE ZERO S AS AN EXTENTION OF PRIME SUBACTS. AMONG THIS WE DEFINE AND STUDY 2-ABSORBING AND STRONGLY 2-ABSORBING IDEALS OF A MONOIDS WHICH IS A GENERALIZATION OF PRIME IDEAL OF SEMIGROUP.

LET R BE A COMMUTATIVE RING. THE TOTAL GRAPH OF R, DENOTED BY T (G(R)), IS A GRAPH WITH ALL ELEMENTS OFR AS VERTICES, AND TWO DISTINCT VERTICES X&NBSP;+ Y&NBSP;Î R ARE ADJACENT IF AND ONLY IF X+ Y&NBSP;Î Z(R), WHERE Z(R) DENOTES THE SET OF ZERO-DIVISORS OF R. IN THIS PAPER, WE STUDY SOME BASIC PROPERTIES OF THE TOTAL GRAPH OF RINGS OF FRACTIONS.

IN THIS TALK WE STUDY MINIMAL FREE RESOLUTIONS OF MAX-PATH IDEALS OF ROOTED TREES BY THE MAPPING CONE TECHNIQUE. IN PARTICULAR WE COMPUTE THE REGULARITY AND PROJECTIVE DIMENSION OF THIS CLASS OF IDEALS.

LETI BE A SUMMATION-TYPE TOPOLOGICAL INDEX AND LET G BE A GRAPH. THE I-COMPLEXITY CI(G) OF GIS INTRODUCED AS THE NUMBER OF DIFFERENT CONTRIBUTIONS TO I (G) IN ITS SUMMATION FORMULA. THE COMPLEXITY IS STUDIED IN THE CASE OF THE CONNECTIVE ECCENTRIC INDEXCE AND SZEGED INDEX. IT IS PROVED THAT CCE(G) £ OV(G) AND CSZ(G) £ OE(G) WHERE OV(G) AND OE(G) ARE THE NUMBER OF DIFFERENT VERTEX ORBITS AND EDGE ORBITS OFG RESPECTIVELY. GRAPHS WITH CCE(G) =1 AND CSZ(G) =1 ARE STUDIED.

LET&NBSP;I&NBSP;BE A SEMI-PRIME IDEAL. PO Î MIN (I) IS CALLED IRREDUNDANT WITH RESPECT TO I IF I, ¹&NBSP;∩&NBSP; PO¹PÎMIN(I) P.IFI IS THE INTERSECTION OF ALL IRREDUNDANT IDEALS WITH RESPECT TO I, IT IS CALLED A FIXED-PLACE IDEAL. IF THERE ARE NO IRREDUNDANT IDEALS WITH RESPECT TOI, IT IS CALLED AN ANTI FIXED-PLACE IDEAL. WE SHOW THAT EACH SEMI-PRIME IDEAL HAS A UNIQUE PRESENTATION AS AN INTERSECTION OF A FIXED-PLACE IDEAL AND AN ANTI FIXED-PLACE IDEAL. WE ALSO PROVE THAT ZERO IDEAL OF A REDUCED RINGR IS ANTI FIXED-PLACE IDEAL (FIXEDPLACE IDEAL) IF AND ONLY IF MIN (R) WITH ZARISKI TOPOLOGY HAS NO ISOLATED POINT (THE SET OF ALL ISOLATED POINTS OF MIN (R) WITH ZARISKI TOPOLOGY IS DENSE IN MIN (R)).

IN THIS WORK, FIRST WE GIVE A CHARACTERIZATION OFN-ABELIAN GROUP G USING THE NOTATION VAR G WHICH IS THE SMALLEST VARIETY CONTAINING THE GROUP G. SECONDLY, WE FIND SOME INTERESTING RESULTS OF THE BOX-TENSOR PRODUCTS OF SUCH GROUPS. FINALLY, WE OBTAIN SOME PROPERTIES OF GROUPS WITHN-ABELIAN NON-ABELIAN TENSOR SQUARE.

LET RL BE THE RING OF REAL-VALUED CONTINUOUS FUNCTIONS ON A FRAME L. THE MAIN AIM OF THIS PAPER IS TO PRESENAT POINTFREE VERSION OF IMAGE OF CONTINUOUS FUNCTIONS WITH FINITE IMAGES IN RL. ALSO, WE INTRODUCE ZF-IDEASL AND ZF-FILTERS.

IN THIS PAPER THE NOTION OF REES SHORT EXACT SEQUENCE FOR S -POSETS IS INTRODUCED, AND THE CONDITIONS FOR A REES SHORT EXACT SEQUENCE OF S -POSETS TO BE LEFT OR RIGHT SPLIT ARE GIVEN. UNLIKE THE CASE FOR S-ACTS, BEING RIGHT SPLIT DOES NOT IMPLY LEFT SPLIT. FURTHERMORE, WE STUDY THE RELATIONSHIP BETWEEN PROJECTIVITY AND THE FUNCTOR HOM (P, −).

FOR AN ASSOCIATIVE RINGR, THE DIRECTED ZERO-DIVISOR GRAPH OF R IS THE GRAPH G(R) SUCH THAT THE VERTICES OF G(R) ARE ALL THE NONZERO ZERO-DIVISORS OF R AND X ® Y IS AN EDGE BETWEEN DISTINCT VERTICES X ANDY IF AND ONLY IF XY=0. OUR GOAL IN THIS NOTE IS TO GIVE A CHARACTERIZATION OF THE POSSIBLE OF DIAM (G(R [X;A,D])) IN TERMS OF DIAM (G(R)), WHEN THE BASE RING R IS REVERSIBLE AND ALSO HAVE THE (A,D) -COMPATIBLE PROPERTY. &NBSP;

SCHUR MULTIPLIER, NON-ABELIAN TENSOR PRODUCT AND CAPABILITY ARE NOTIONS IN GROUP THEORY HAVING CLOSE RELATIONSHIP. IN THIS TALK WE INTEND TO SHOW HOW SCHUR MULTIPLIER AND NON-ABELIAN TENSOR PRODUCT CAN HELP DETECTING THE CAPABILITY OF GROUPS.

IN THE PRESENT PAPER, BY CONSIDERING THE DEFINITION OF HYPERVALUATION OF A HYPERRING ONTO A TOTALLY ORDERED GROUP, WE STUDY SOME PROPERTIES OF HYPERVALUATIONS AND OBTAIN SOME RELATED BASIC RESULTS.

LET (R, M) BE A LOCAL NOETHERIAN RING AND LET E BE AN INJECTIVE R-MODULE. IT IS SHOWN THAT WHEN E IS MATLIS REFLEXIVE &NBSP;

THE ANNIHILATING-IDEAL GRAPH OF A COMMUTATIVE RINGR, DENOTED BY AG (R), IS A GRAPH WHOSE VERTEX SET CONSISTS OF ALL NON-ZERO ANNIHILATING IDEALS AND TWO DISTINCT VERTICES ARE ADJACENT IF AND ONLY IF THEIR PRODUCT IS ZERO. HERE, SOME CRITERIA FOR A GRAPH TO BE ISOMORPHIC WITH AN ANNIHILATING-IDEAL GRAPH OF A RING, IS GIVEN. ANNIHILATING-IDEAL GRAPHS WHICH ARE TREES ARE SPECIFIED. SOME RESULTS ABOUT THE VERTICES WITH MAXIMUM DEGREE ARE STATED, TOO. FINALLY, IT IS SHOWN THAT THE INDUCED SUBGRAPH OF AG(R) ON VERTICES WITH MAXIMUM DEGREE IS EITHER COMPLETE OR A DISCRETE GRAPH.

IN THIS PAPER, WE FIRST INTRODUCE A NEW WEIGHTED GENERALIZATION OF THE CLIQUE POLYNOMIALS. THEN, WE SHOW THAT FOR ANY CHOICES OF NON-NEGATIVE WEIGHTS THESE NEW GRAPH POLYNOMIALS HAVE ALWAYS A REAL ROOT. FINALLY, WE OBTAIN A NO-HOMOMORPHISM CRITERIA BASED ON THE GREATEST REAL ROOT OF OUR WEIGHTED CLIQUE POLYNOMIALS.

IN THIS PAPER, WE CONSIDER CHORDAL CLUTTERS AS IT IS DEFINED IN [7] AND [1] VIA SIMPLICIAL ORDERS. THE MAIN IMPORTANCE OF THE CHORDAL CLUTTERS IN THIS SENSE IS THAT THEIR CIRCUIT IDEAL HAS A LINEAR RESOLUTION, INDEPENDENT OF THE CHARACTERISTIC OF THE BASE FIELD. ASSOCIATED WITH ANY SIMPLICIAL ORDER IS A SEQUENCE OF INTEGERS WHICH WE CALL THE-SEQUENCE OF THE CHORDAL CLUTTER. ALL POSSIBLE -SEQUENCES ARE CHARACTERIZED. BY THE-SEQUENCE OF A CHORDAL CLUTTER WE DETERMINE OTHER NUMERICAL INVARIANTS OF THE CIRCUIT IDEAL, SUCH AS THEH-VECTOR AND THE BETTI NUMBERS. WE ALSO SHOW THAT ANY BETTI SEQUENCE OF AN IDEAL WITH LINEAR RESOLUTION APPEARS AS THE BETTI SEQUENCE OF THE CIRCUIT IDEAL OF SUCH A CHORDAL CLUTTER.

THE CATEGORYNOM, OF ALL FINITELY SUPPORTED G-SETS, CALLED THE G-NOMINAL SETS, WHERE G=PERMF(D) IS THE GROUP OF FINITARY PERMUTATIONS OVER A COUNTABLE INFINITE SET D, IS A SUBJECT OF INTEREST BY BOTH SET THEORISTS AND COMPUTER SCIENTISTS. THE CATEGORY 01-NOM, OF ALL G-NOMINAL SETS EQUIPPED WITH THE SOURCE AND THE TARGET OPERATIONS, WAS INTRODUCED BY PITTS.IN THIS PAPER, WE STUDY THE EXISTENCE OF THE FREE OBJECTS IN THE CATEGORY 01-NOM OVER G-NOMINAL SETS.

LET L BE A LIE ALGEBRA AND ID(L) BE THE SET OF ALL DERIVATIONS OF L WHOSE IMAGES LIE IN THE DRIVED ALGEBRA OFL. IN THIS PAPER, THE CENTRAL IDEAL S(L) = {X 2 L |A(X) =0, NA Î ID(L)} OF A LIE ALGEBRA L IS STUDIED. WE PROVE SOME RESULTS ANALOGOUS TO A RESULT BY SCHUR AND A WEAK FORM OF ITS CONVERSE IN THE CONTEXT OF ID-DERIVATIONS. ALSO, WE GIVE AN UPPER BOUND FOR DIMENSION OF L / S(L) IN SOME SPECIAL CONDITIONS. &NBSP;

LET R BE A COMMUTATIVE NOETHERIAN RING, A AN IDEAL OF R AND D(R) DENOTE THE DERIVED CATEGORY OF R-MODULES.WE ARE GOING TO FIND AN UPPER BOUND FOR SUP LLA(X) IN THIS PAPER. FOR ANY HOMOLOGICALLY BOUNDED COMPLEX X, WE CONJECTURE THAT SUP LLA(X) £ MAGRX. WE PROVE THIS IN SEVERAL CASES.

A FINITE GROUP G IS CALLED A RATIONAL GROUP IF ALL THE GENERATORS OF EVERY CYCLIC SUBGROUP OF G ARE CONJUGATE. IN THIS ARTICLE WE DISCUSS ABOUT NILPOTENCY CLASS OF RATIONAL 2-GROUPS AND WE GIVE AN UPPER BOUND FOR NILPOTENCY CLASS OF A RATIONAL GROUPG OF ORDER 2N. FURTHERMORE WE SHOW THAT AN IRREDUCIBLE CHARACTERC OF A RATIONAL 2-GROUP G DOES NOT APPEAR AS A CONSTITUENT OF CHARACTER C2 EXCEPT FOR C=1G, THE PRINCIPAL CHARACTER OF G.

FOR A PROPER SUBALGEBRAH OF A LIE ALGEBRA L, WE SAY A SUBALGEBRA C OF L IS A Q-COMPLETION FOR H IF L=< H, C >WHILE HL £ C AND IF C1/HL IS A PROPER SUBALGEBRA OF C/HL SUCH THAT C1/HL&NBSP; &NBSP;L/HL, THEN&NBSP;L ¹ &NBSP;H + C1. A Q-COMPLETION C OF H IS CALLED S-Q-COMPLETION, IF C=L OR THERE EXISTS A SUBALGEBRAB OF L SUCH THAT C L B AND B IS NOT A Q-COMPLETION FOR H. BY THESE NOTIONS WE GIVE SOME CHARACTERISATIONS FOR SOLVABILITY OF LIE ALGEBRAS.

THE CONCEPTS OF SOFT HYPERMODULES AND SOFT FUZZY HYPERMODULES ARE INTRODUCED BY APPLYING SOFT SET THEORY TO HYPERMODULES AND FUZZY HYPERMODULES. ALSO, THE CONNECTION BETWEEN SOFT HYPERMODULES AND SOFT FUZZY HYPERMODULES IS VERIFIED BY ASSOCIATED (FUZZY) HYPEROPERATIONS AND HOMOMORPHISMS.

GIVEN A GROUPG, A SUBGROUP AGN IS DEFINED AS AGN=Á[X,AN] | X&NBSP;Î G,&NBSP;A Î AUT (G)Ñ. G IS CALLED N-CHARACTERISTIC GROUP IF AGN=1 FOR SOME N 2 N. IN THE ARTICLE WE DETERMINE THE STRUCTURE OF AGN IN AUTONILPOTENT GROUPS OF CLASS C < 5 AND AMONG OTHER RESULTS WE PROVE G IS AN ABELIAN 2-CHARACTERISTIC AUTONILPOTENT GROUP OF CLASS 3 IF AND ONLY IF G @ C8.

THE SOLVABLE GRAPH OF A FINITE GROUPG, DENOTED BY GS (G), IS A SIMPLE GRAPH WHOSE VERTICES ARE THE PRIME DIVISORS OF|G| AND TWO DISTINCT PRIMES P AND Q ARE JOINED BY AN EDGE IF AND ONLY IF THERE EXISTS A SOLVABLE SUBGROUP OFG SUCH THAT ITS ORDER IS DIVISIBLE BY PQ. LET P1 < P2 < · · · <PK BE ALL PRIME DIVISORS OF |G| AND LET DS(G) = (DS (P1), DS (P2), ..., DS (PK)), WHERE DS(P) SIGNIFIES THE DEGREE OF THE VERTEXP IN GS(G). WE WILL SIMPLY CALL DS(G) THE DEGREE PATTERN OF SOLVABLE GRAPH OF G. THE PURPOSE OF THIS ARTICLE IS TWOFOLD. FIRST, IT PROVIDES THE STRUCTURE OF ANY FINITE GROUP G (UP TO ISOMORPHISM) FOR WHICH GS(G) IS STAR OR BIPARTITE. SECOND, IT IS PROVED THAT THE SPORADIC SIMPLE GROUPS AND SOME OF PROJECTIVE SPECIAL LINEAR GROUPS L2(Q) ARE CHARACTERIZED VIA ORDER AND DEGREE PATTERN OF SOLVABLE GRAPHS.

LETG BE A GROUP AND G0 BE ITS COMMUTATOR SUBGROUP. DENOTE BY C (G) THE MINIMAL NUMBER SUCH THAT EVERY ELEMENT OF G0 CAN BE EXPRESSED AS A PRODUCT OF AT MOST C (G) COMMUTATORS. A GROUP G IS CALLED A C-GROUP IFC (G) IS FINITE. ...

THE OVERALL AIM OF THIS PAPER IS TO PRESENT AN INTRODUCTION TO SOME OF THE RESULTS, METHODS AND IDEAS ABOUT SEMIHYPERGROUPS, HYPERGROUPS, HYPERRINGS AND FUNDAMENTAL RELATIONS. WE PRESENT THE RECENT PROGRESS IN THE THEORY OF ALGEBRAIC HYPERSTRUCTURES, MOST OF WHICH REFLECT THE AUTHOR PAST RESEARCH.

THE AIM OF THIS NOTE IS TO DEFINE STRONGLY FIXED IDEALS OF THE RING RL BASED ON ZERO SETS IN POINTFREE TOPOLOGY. FOR WEAKLY SPATIAL FRAMES, THIS DEFINITION IS EQUIVALENT TO THE DEFINITION OF FIXED IDEALS IN RL. ALSO FOR COMPLETELY REGULAR FRAMES, A CHARACTERIZATION OF STRONGLY FIXED MAXIMAL IDEALS IN RL IS PROVIDED.

A SUBSET OF VERTICES IN A HYPERGRAPH H IS AN INDEPENDENT SET IF IT CONTAINS NO EDGE OF H. THE INDEPENDENCE NUMBER, A(H), OF H IS THE MAXIMUM CARDINALITY OF AN INDEPENDENT SET IN H. OUR MAIN RESULT IS AN IMPROVEMENT OF A LOWER BOUND FOR THE INDEPENDENCE NUMBER OF 2-UNIFORM HYPERGRAPHS DUE TO HENNING AND L¨OWENSTEIN (2014) WHO PROVED THAT IFH IS A CONNECTED 2-UNIFORM HYPERGRAPH OF ORDERN AND SIZE M AND H DOES NOT BELONG TO A SPECIFIC FAMILY OF HYPERGRAPHS, THEN A(H)>2/3N − 1/4 M. FURTHER THEY CHARACTERIZE THE HYPERGRAPHSH FOR WHICH A(H) £ 2/3N − 1/4M. IN THIS PAPER WE IMPROVE AFORESAID BOUND FOR CONNECTED 2-UNIFORM HYPERGRAPHS OF MAXIMUM DEGREE AT LEAST FOUR. ALSO WE CHARACTERIZE ALL CONNECTED 2-UNIFORM HYPERGRAPHS ACHEIVING EQUALITY FOR THIS BOUND.

IN THIS PAPER, THE CONCEPT OF ADDITIVE TOPOLOGICAL GENERALIZED GROUP AND TOPOLOGICAL GENERALIZED RING ARE DEFINED AND SOME PROPRTIES OF THEM ARE INVESTIGATED.

IN THIS PAPER WE FIND AN EXPLICIT FORMULA FOR THE NUMBER OF FUZZY SUBGROUP OF FROBENIUSQ- GROUP. THAT RELATION BETWEEN OF CHARACTERS THEORY, GROUP THEORY AND FUZZY GROUP THEORY IS INDICATED. IN THIS WORK, FIRST OF ALL, USING BY THEOREMS IN CHARACTERS THEORY AND GROUP THEORY WE CLASSIFY FROBENIUSQGROUP AND THEN BY [1], WE FIND AN EXPLICIT FORMULA FOR SEMI DIRECT PRODUCT OF A GENERALIZED QUATERNION GROUP OF EIGHT ORDER AND FINITE ELEMENTARY ABELIANP-GROUPS.

LET G BE A GROUP. WE SAY THAT G SATISFIES THE CONDITION T(¥) IF EVERY INFINITE SET OF ELEMENTS OF GCONTAINS THREE DISTINCT ELEMENTS X ¹&NBSP;Y, Z SUCH THAT [X, Y, Z] =1= [Y, Z, X] = [Z, X, Y]. IN THIS PAPER WE SHOW THAT A FINITELY GENERATED RESIDUALLY FINITE (LOCALLY GRADED) GROUPG IS IN T(¥) IF AND ONLY IF G/Z2 (G) IS FINITE.

IN THIS PAPER WE PREPARE ZERO-ELEMENTS IN LATTICE THEORY AS THE IMAGES OF{0} IN THE ¦-RING OF REALVALUED FUNCTIONS ON A FRAME WHICH IS GENERALIZATION OF ALL REAL FUNCTIONS ON A SET X.

IN THIS PAPER, WE STUDY ON TORSION THEORY AND RADICALS IN THE CATEGORY OF S -ACT. WE INTRODUCE THE KUROSH-AMITSUR RADICALS AND THE HOEHNKE RADICALS. WE THEN INVESTIGATE THE RELATIONSHIP BETWEEN HOEHNKE RADICALS AND KUROSH-AMITSUR RADICALS AND WE SHOW THAT THE CLASS OF KUROSH-AMITSUR RADICALS AS A POSET IS A REFLECTIVE SUBCATEGORY OF THE CLASS OF HOEHNKE RADICALS. WE ALSO CHARACTERIZE THE HEREDITARY KUROSH-AMITSUR RADICALS BY THE SEMISIMPLE CLASSES WHICH ARE CLOSED UNDER TAKING INJECTIVE ENVELOP.

IN THIS TALK WE INTEND TO OBTAIN A COVERING SPACE OF QUASITOPOLOGICALNTH HOMOTOPY GROUP OF THE POINTED SPACE (X, X). FOR THIS, WE GIVE A COVERING SPACE OF THE LOOP SPACE WN(X, X) AND WE PRESENT SOME PROPERTIES OF IT.

LET R BE A COMMUTATIVE RING WITH IDENTITY. WE WILL SAY THAT AN R-MODULE M IS IDEAL STABLE, IF IM=M, WHEREI IS AN IDEAL OF R, IMPLIES THAT IX=RX FOR ALL X Î M. IN THIS PAPER, WE WILL STUDY IDEAL STABLE MODULES. AMONG OTHER RESULTS, IT IS PROVED THAT IF R IS AN ARTINIAN RING, THEN EVERY R-MODULE IS IDEAL STABLE AND THE CONVERSE IS TRUE IF R IS NOETHERIAN.

LET G BE A FINITE GROUP AND |CENT2(G)| DENOTES THE NUMBER OF TWO-CENTRALIZERS OF ITS ELEMENTS. A GROUP G IS CALLED N-TWO-CENTRALIZER IF |CENT2(G)| = N. IN THE PRESENT ARTICLE WE SHOW THERE EXISTS A FINITEN-TWO-CENTRALIZER GROUP FOR ANY NATURAL NUMBER N.

LET I BE AN IDEAL OF A COMMUTATIVE NOETHERIAN RING R. IN THIS PAPER WE OBTAIN SOME LYUBEZNIK TABLES FOR CERTAIN RINGS AND MODULES.

IN THIS PAPER, WE INTRODUCE THE CONCEPTS OF UPPER ROUGH FUZZY IDEALS AND UPPER ROUGH FUZZY PRIME IDEALS (FILTERS) IN A HYPERLATTICE AND ITS BASIC PROPERTIES ARE DISCUSSED.

THE MAIN INTEREST IN THIS ARTICLE IS THE QUESTION OF DETERMINING MONOMIAL IDEALS SUCH THAT THE BLOWUP OF THE AFFINE SPACE ANK ALONG THESE IDEALS IS REGULAR. WE SHOW THAT THE BLOWUP OF THE AFFINE SPACE ANK ALONG A SQUARE FREE MONOMIAL IDEALI IS REGULAR IF AND ONLY IF THE CORRESPONDING CLUTTER (HYPERGRAPH) ASSOCIATED TOI IS A UNION OF SOME ISOLATED VERTICES AND A COMPLETE D-PARTITE D-UNIFORM CLUTTER. THIS IS EQUIVALENT TO SAYING THAT THE FACETS OF ITS STANLEY-REISNER COMPLEX HAVE MUTUALLY DISJOINT COMPLEMENTS. FINALLY WE CLASSIFY ALL MONOMIAL IDEALS GENERATED IN DEGREE AT MOST 2 SUCH THAT THE BLOWUP OF THE AFFINE SPACE ANK ALONG THESE IDEALS IS REGULAR.

FOR TWO GIVEN NON-NEGATIVE INTEGERS J AND K, A DOMINATING SET S OF A GRAPH G IS A TOTAL [J, K] -SET IF EACH VERTEX OF V (G) IS DOMINATED BY AT LEAST J, BUT NOT MORE THAN K VERTICES OF S. THE CARDINALITY OF THE SMALLEST SUCH SET IS DENOTED BY G[J, K](G). IN THIS PAPER, WE INVESTIGATE THE EXISTENCE OF SUCH DOMINATIONS FOR CORONA PRODUCT OF GRAPHS. MOREOVER, WE DESCRIBE TOTAL [1, K] -SETS OF CARTESIAN PRODUCTS GH FOR ARBITRARY GRAPHS G AND H. ALSO, WE GIVE SOME SUFFICIENT CONDITIONS FOR G AND H SUCH THAT THE STRONG PRODUCT G H HAS A TOTAL [1, K] -SET.

IN THIS PAPER WE INTRODUCE THE ASCENDING FUZZYN-CENTERAL SERIES OF FUZZY SUBGROUP OF A GIVEN GROUP. ALSO, WE INTRODUCE THE CONCEPT OFN-NILPOTENT FUZZY SUBGROUP AND INVESTIGATE THE PROPERTIES OF NNILPOTENT FUZZY SUBGROUP OF A GROUP G.

H-BASES ARE A PARTICULAR KIND OF BASES FOR POLYNOMIAL IDEALS, CHARACTERIZED BY THE FACT THAT THEIR HOMOGENEOUS LEADING TERMS ARE A BASIS FOR THE ASSOCIATED HOMOGENEOUS IDEAL. IN THE COMPUTATION OF H-BASES, THE MAIN OBSTACLE IS TO DETERMINE A SYSTEM OF GENERATORS FOR EACH UNDER CONSIDERATION SYZYGY MODULE. THE ONLY KNOWN METHOD TO DOING SO, IS BASED ON THE GROBNER BASES COMPUTATION WHICH MAKES THE COMPUTATION OF H-BASES FAR FROM EFFICIENCY. IN THIS PAPER, WE PRESENT AND STUDY AN EFFICIENT METHOD TO COMPUTE H-BASES WITHOUT RELYING ON THE GROBNER BASES CALCULATION.

IN THIS PAPER, WE INTRODUCE THE NOTION OF INTUITIONISTIC FUZZY IDEALS OF BN-ALGEBRAS AND SOME PROPERTIES OF THEM ARE GIVEN, ALSO WE GIVE THE RELATIONSHIP BETWEEN INTUITIONISTIC FUZZY IDEAL AND (FUZZY) IDEAL OF BN-ALGEBRAS. FINALLY, WE CONSTRUCT THE LATTICE OF INTUITIONISTIC FUZZY IDEALS OF BN-ALGEBRAS.

IN THIS PAPER WE INTRODUCE THE CONCEPT OF FUZZY SCHUR MULTIPLIER SUBGROUP OF A FUZZY SUBGROUP

LET R BE A COMMUTATIVE NOETHERIAN RING, LET A BE AN IDEAL OF R; AND LET S BE A SUBCATEGORY OF THE CATEGORY OF R-MODULES. IN THIS PAPER, WE DEFINE AND STUDY THE CLASS SA CONSISTING OF ALL MODULES SATISFYING THE CONDITION CA. IF A AND B ARE IDEALS OF R, WE GET A NECESSARY AND SUFFICIENT CONDITION IN ORDER THAT S SATISFIES THE CONDITIONS CA AND CB SIMULTANEOUSLY. WE ALSO FIND SOME SUFFICIENT CONDITIONS UNDER WHICHS SATISFIES CA. WE INVESTIGATE WHEN LOCAL COHOMOLOGY MODULES LIE IN A SERRE SUBCATEGORY.

LET R BE A NOETHERIAN DOMAIN AND M BE A FINITELY GENERATED R-MODULE. LET FITT R(M) BE THE FIRST FITTING IDEAL OF M. THE MAIN RESULT OF THIS PAPER IS TO CHARACTERIZE ALL R-MODULES M WHEN FITT R(M) IS A PRODUCT OF MAXIMAL IDEALS OF HEIGHT AT MOST TWO.

IN THIS PAPER WE INVESTIGATE THE ACTIONS OF A MONOID OF THE FORM S=G Ů I, WHERE G IS A GROUP AND I IS AN IDEAL OFS, ON SETS. SO, NATURALLY, EVERY S -ACT CAN BE CONSIDERED AS AN I1-ACT. THE CENTRAL QUESTION HERE IS THAT WHAT IS THE RELATION BETWEEN ABSOLUTE 1-PURITY OF I1-ACTS AND ABSOLUTE 1-PURITY OF S -ACTS. HERE WE RESPOND TO THIS QUESTION AND SHOW THAT WE NEED SOME MORE HYPOTHESIS.

IN THIS ARTICLE, WE STATE A NEW SYMBOLIC-NUMERIC APPROACH TO SOLVE AND ANALYZE A SYSTEM OF DIFFERENTIAL EQUATIONS USING GROBNER BASIS. THE NEW APPROACH PROVIDES THE SOLUTION IN THE FORM OF A RAPIDLY CONVERGENT SERIES WITH EASILY COMPUTABLE COMPONENTS USING SYMBOLIC COMPUTATION METHODS. THE PROPOSED TECHNIQUE IS APPLIED TO SEVERAL TEST PROBLEMS TO ILLUSTRATE THE ACCURACY AND EFFICIENTCY OF THE METHOD.