Let R be a commutative Noetherian ring, I⊆ J be ideals of R and M be a finitely generated R-
module. In this paper it is shown that q (J, M)≤ q (I, M)+ cd (J, M/IM). Furthermore, it is shown …

Let $ R $ be a commutative Noetherian ring, $\fa $ an ideal of $ R $, $ M $ and $ N $ be two
finitely generated $ R $-modules. Let $ t $ be a positive integer. We prove that if $ R $ is …

Let R be a commutative Noetherian ring with nonzero identity, 𝔞 an ideal of R, M a finite R–
module, X an arbitrary R–module, and na non-negative integer. Here, we show that, in the …

We study the relative Gorenstein projective global dimension of a ring with respect to a
weakly Wakamatsu tilting module C. We prove that this relative global dimension is finite if …

Let R be a ring with an identity and, for a left Λ-module RM, pd (M) and ίd (M) denote the
projective and injective dimension of RM, respectively. A (left and right) noether ring R is …

In this paper, we introduce and study a notion of Gorenstein AC-injective dimension for
complexes of left modules over associative rings. We show first that the class of complexes …

In the derived category of the category of modules over a commutative Noetherian ring R,
we define, for an ideal 𝔞 of R, we investigate the interplay between the two naturally defined …

It is well-known that the ith local cohomology of a finitely generated R-module M over a
positively graded commutative Noetherian ring R, associated to the irrelevant ideal R+ is …

In 1966, Auslander introduced the notion of the $ G $-dimension of a finitely generated
module over a Cohen-Macaulay noetherian ring and found the basic properties of these …

Let R be a commutative Noetherian ring, Φ a system of ideals of R and I∈ Φ. In this paper
among other things we prove that if M is finitely generated and t∈ N such that the R-module …