We study homological aspects of Gorenstein flat modules over a ring with respect to a
duality pair (L, A). These modules are defined as cycles of exact chain complexes with …

Let $ A $ be an Artin algebra, $ M $ be a Gorenstein projective $ A $-module and $ B= $ End
$ _A M $, then $ M $ is a $ A $-$ B $-bimodule. We use the restricted flat dimension of …

A complex C is called Gorenstein injective if there exists an exact sequence of
complexes⋯→ I− 1→ I0→ I1→⋯ such that each Ii is injective, C= Ker (I0→ I1) and the …

Throughout this paper, if not specified otherwise, R denotes an associative ring with identity
and all modules are unital left R-modules. Every result given for left modules has a …

We will study modules of the highest injective, projective and flat dimension over a
Goresntein ring. Let R be a Gorenstein ring of self-injective dimension n and 0–RR→ E0 …

Let SCR be a semidualizing bimodule with S left coherent and R right coherent. For a non-
negative integer n, it is shown that l. FP-id S (C)= r. FP-id R (C)≤ n if and only if every finitely …

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 …

In these expository notes I discuss several concepts and results in the theory of modules
over commutative rings, revolving around the Gorenstein dimension of modules. Some of …

Let (R, m) be a commutative Noetherian local ring of Krull dimension d, and let C be a
semidualizing R-module. In this paper, it is shown that if R is complete, then C is a dualizing …

In this paper, we further study Gorenstein dimension over local homomorphisms developed
by Iyengar and Sather-Wagstaff. For a local homomorphism φ: R→ S and a homologically …