There are different approaches to characterizing the structures of commutative rings: the
category of modules over commutative rings, homology theories, theories of the star …

In this paper, we study certain properties of modules of finite Gorenstein projective, injective
and flat dimensions. We examine conditions which imply that all Gorenstein projective …

In this paper, we study the relative homological dimension based on the class of projectively
coresolved Gorenstein flat modules (PGF-modules), that were introduced by Saroch and …

Starting from the notion of totally reflexive modules, we survey the theory of Gorenstein
homological dimensions for modules over commutative rings. The account includes the …

Let 𝒜 be an abelian category having enough projective and injective objects, and let 𝒯 be
an additive subcategory of 𝒜 closed under direct summands. A known assertion is that in a …

In this paper, we investigate the weak Gorenstein global dimension. We are mainly
interested in studying the problem when the left and right weak Gorenstein global …

For a commutative ring R and a faithfully flat R-algebra S we prove, under mild extra
assumptions, that an R-module M is Gorenstein flat if and only if the left S-module S⊗ RM is …

Abstract Distinctive characteristics of Iwanaga–Gorenstein rings are typically understood
through their intrinsic symmetry. We show that several of those that pertain to the Gorenstein …

We introduce relative preresolving subcategories and precoresolving subcategories of an
abelian category and define homological dimensions and codimensions relative to these …

Let R be a commutative ring. An R-module M is said to be super finitely presented if there is
an exact sequence of R-modules where each P i is finitely generated projective. In this …