JOURNAL OF ALGEBRAIC SYSTEMS
Year:2016 | Volume:3 | Issue:2 |Papers Count:10

The purpose of carrying out this work is to develop the amenability notations for vector-valued group algebras. We prove that L1(G; A) is approximately weakly amenable where A is a unital separable Banach algebra. We give the necessary, and sufficient conditions for the existence of a left invariant mean on L1(G; A ), LUC(G; A ), WAP(G; A ), and C0(G; A ).

In this work, we attempt to investigate the connection between various types of ideals (for examples (m; n)-ideal, bi-ideal, interior-ideal, quasi-ideal, prime-ideal and maximal-ideal) of an or-dered semigroup (S;
;  ) and the corresponding, hyperideals of its EL-hyperstructure (S;  ) (if exists). Moreover, we construct the class of EL-􀀀-semihypergroup, associated to a partially-ordered 􀀀-semigroup.

Let G be a  nite p-group. In this work we give the necessary and sufficient conditions on G such that each absolute central automorphism of G  xes the center element-wise. Also we classify all groups of the orders p3 and p4, whose absolute central automorphisms  x the center element-wise.

Let R = ⊕ n2N0 Rn be a standard graded ring, M be a  nitely-generated graded R-module, and J be a homogeneous ideal of R. In this work, we study the graded structure of the i-th local cohomology module of M, de ned by a pair of ideals (R+; J), i. e. Hi R+; J (M). More precisely, we discuss the  niteness property and vanishing of the graded components Hi R+; J (M)n. Also, we study the Artinian property and tameness of certain submodules and quotient modules of Hi R+; J (M).

Let (R; m) be a commutative Noetherian local ring, and M be a non-zero  nitely-generated R-module. We show that if R is almost Cohen-Macaulay andM is perfect with  nite projective dimension, then M is an almost Cohen-Macaulay module. Also, we give some necessary and sufficient conditions on M to be an almost Cohen-Macaulay module, by using Ext functors.

The aim of this work is to compute the rational character tables of the dicyclic group T4n, the groups of the orders pq and pqr. Some general properties of rational character tables are also considered.

By left magma-e-magma, I mean a set containing a  xed element e, and equipped with the two binary operations \
" and ⊙ , with the property of e⊙ (x
y) = e⊙ (x⊙ y), namely the left e-join law. Thus (X;
; e; ⊙ ) is a left magma-e-magma if and only if (X;
) and (X; ⊙ ) are magmas (groupoids), e 2 X and the left e-join law holds. The right and two-sided magma-e-magmas are de ned in an analogous way. Also X is a magma-joined-magma if it is magma-x-magma for all x 2 X. Therefore, I introduce a big class of basic algebraic structures with two binary operations, some of whose sub-classes are group-e-semigroups, loop-e-semigroups, semigroup-e-quasigroups and etc. A nice in nite (resp.  nite) example of them is the real group-grouplike (R; +; 0; +1) (resp. Klein group-grouplike). In this paper, I introduce and study the topic, construct several big classes of such algebraic structures and characterize all the identical magma-e-magmas in several ways. The motivation of this study lies in some interesting connections to f-multiplications, some basic functional equations on algebraic structures and Grouplikes (recently introduced by me). Finally, I present some directions for the researches conducted on the sub-ject.

In this paper, we introduce a new class of modules that is closely related to the class of Noetherian modules. Let R be a commutative ring with identity, and M be an R-module such that Nil(M) is a divided prime submodule of M. M is called a nonnil-Noetherian R-module if every nonnil submodule of M is  nitely-generated. We prove that many properties of the Noether-ian modules are also true for the nonnil-Noetherian modules.

Let (R; m) be a Gorenstein local ring, and M and N be two  nitely-generated modules over R. Nagel proved that if M and N are in the same even liaison class, then one has Hi m(M)  = H im (N) for all i < dimM = dimN. In this paper, we provide a short proof to this result.

Let R be a commutative Noetherian ring, a be an ideal of R, and D(R) denote the derived category of R-modules. For any homologically-bounded complex X, we conjecture that supL a(X)  magRX. We prove this in several cases.