Let (R,m) be a commutative Noetherian local ring. We establish some bounds for the sequence of Bass numbers and their dual for a finitely generated R-module. Introduction Throughout this paper, (R,m, k) is a non-trivial commutative Noetherian local ring with unique maximal ideal m and residue field k. Several authors have obtained results on the growth of the sequence of Betti numbers {βn(k)} (...

We introduce the class of “right almost V-rings” which is properly between the classes of right V-rings and right good rings. A ring R is called a right almost V-ring if every simple R-module is almost injective. It is proved that R is a right almost V-ring if and only if for every R-module M, any complement of every simple submodule of M is a direct summand. Moreover, R is a right almost V-rin...

The concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. The notion of free fuzzy modules was introducedby Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameriintroduced the concept of projective and injective L-modules. In this paper we give analternate definition for projective L-modules. We prove that e...

Let be a commutative Noetherian ring and let I be a proper ideal of . D’Anna and Fontana in [6] introduced a new construction of ring,  named amalgamated duplication of along I. In this paper by considering the ring homomorphism , it is shown that if , then , also it is proved that if , then there exists  such that . Using this result it is shown that if is generically Cohen-Macaulay (resp. gen...

This paper is a continuation of the papers J. Pure Appl. Algebra, 210 (2007), 437–445 and J. Algebra Appl., 8 (2009), 219–227. Namely, we introduce and study a doubly filtered set of classes of modules of finite Gorenstein projective dimension, which are called (n, m)-strongly Gorenstein projective ((n, m)-SG-projective for short) for integers n ≥ 1 and m ≥ 0. We are mainly interested in studyi...

we introduce the class of “right almost v-rings” which is properly between the classes of right v-rings and right good rings. a ring r is called a right almost v-ring if every simple r-module is almost injective. it is proved that r is a right almost v-ring if and only if for every r-module m, any complement of every simple submodule of m is a direct summand. moreover, r is a right almost v-rin...