JOURNAL OF ALGEBRAIC SYSTEMS
Year:2017 | Volume:5 | Issue:1 |Papers Count:7

In the present paper, by considering the notion ofMV-modules which is the structure that naturally correspond to lu-modules over lu-rings, we prove some results on prime A-ideals and state some conditions to obtain a prime A-ideal in MV-modules. Also, we state some conditions that an A-ideal is not prime and investigate conditions that K  ∪ n i=1 Ki implies K  Kj, where K; K1;


; Kn are A-ideals of A-module M and 1  j  n.

Using a system of axioms among with a modi ed def-inition of boundary on the basis of the intuitionistic fuzzy sets, we formulate an inductive structure for the dimension of fuzzy spaces which has been de ned by Coker. This new de nition of boundary allows to characterize an intuitionistic fuzzy clopen set as a set with zero boundary. Also, some critical properties and applications are established.

Let G be a  nite group and C(G) be a family of representative conjugacy classes of subgroups of G. The matrix whose H; K-entry is the number of  xed points of the set G=K under the action of H is called the table of marks of G, where H; K run through all elements in C(G). In this paper, we compute the table of marks and the markaracter table of groups of order pqr, where p, q, r are prime numbers.

Let (R; m) be a commutative noetherian local ring and 􀀀 be a  nite group. It is proved that if R admits a dualiz-ing module, then the group ring R􀀀 has a dualizing bimodule, as well. Moreover, it is shown that a  nitely generated R􀀀-module M has generalized Gorenstein dimension zero if and only if it has generalized Gorenstein dimension zero as an R-module.

In this paper, we study almost uniserial rings and modules. An R􀀀 module M is called almost uniserial if any two non-isomorphic submodules of M are linearly ordered by inclusion. A ring R is an almost left uniserial ring if RR is almost uniserial. We give some necessary and sufficient condition for an Artinian ring to be almost left uniserial.

Let R be a commutative ring with identity. The pur-pose of this paper is to introduce and study two classes of modules over R, called Max-injective and Max-strongly top modules and explore some of their basic properties. Our concern is to extend some properties of X-injective and strongly top modules to these classes of modules and obtain some related results.

The aim of this paper is to obtain the automorphism group of the commuting graph of a conjugacy class in the sym-metric groups. The clique number, coloring number, independence number and diameter of these graphs are also computed.