Let 𝔞 be an ideal of a commutative Noetherian ring R and M and N two finitely generated R-
modules. Let cd𝔞 (M, N) denote the supremum of the i's such that. First, by using the theory …

In this paper we will first establish a duality between in jectivity and flatness for modules.
That is: Let E be a faithfully in jective module". Then, for each module A, we have W, dim. A …

It is well-known that a ring R is semiperfect if and only if RR (or RR) is a supplemented
module. Considering weak supplements instead of supplements we show that weakly …

This article centers around artinianness of the local cohomology of ZD-modules. Let a he an
ideal of a commutative Noetherian ring R. The notion of a-relative Goldie dimension of an R …

For a Noetherian local ring, the prime ideals in the singular locus completely determine the
category of finitely generated modules up to direct summands, extensions and syzygies …

Let $\mathfrak a $ be an ideal of a commutative Noetherian ring $ R $. For finitely generated
$ R $-modules $ M $ and $ N $ with $\operatorname {Supp} N\subseteq\operatorname …

We prove that over a commutative noetherian ring the three approaches to introducing depth
for complexes: via Koszul homology, via Ext modules, and via local cohomology, all yield the …

In the last years (Gorenstein) homological dimensions relative to a semidualizing module C
have been subject of several works as interesting extensions of (Gorenstein) homological …

We prove that the category of modules cofinite with respect to an ideal of dimension one in a
noetherian ring is a full abelian subcategory of the category of modules. The proof is based …