We introduce and investigate the notion of 𝐺𝐶-projective modules over (possibly non-
Noetherian) commutative rings, where 𝐶 is a semidualizing module. This extends Holm and …

Cohen-Macaulay dimension for modules over a commutative ring has been defined by AA
Gerko. That is a homological invariant sharing many properties with projective dimension …

Gorenstein homological dimensions are refinements of the classical homological
dimensions, and finiteness singles out modules with amenable properties reflecting those of …

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 …

This book is intended as a reference for mathematicians working with homological
dimensions in commutative algebra and as an introduction to Gorenstein dimensions for …

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 …

A semi-dualizing module over a commutative noetherian ring A is a finitely generated
module C with RHomA (C, C)≃ A in the derived category D (A). We show how each such …

A central problem in the theory of Gorenstein dimensions over commutative noetherian rings
is to find resolution-free characterizations of the modules for which these invariants are finite …

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 this article, we study V-Gorenstein modules relatives to a dualizing module (Enochs et
al.,). These modules constitute a generalization of the well-known Gorenstein modules and …