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 …

In this article, we study the relation between m-strongly Gorenstein projective (resp.,
injective) modules and n-strongly Gorenstein projective (resp., injective) modules whenever …

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 …

Let R be a commutative Noetherian ring and A an Artinian R-module. We prove that if A has
finite Gorenstein injective dimension, then A possesses a Gorenstein injective envelope …

Let S and R be rings and SCR a semidualizing bimodule. We investigate the relation
between the GC-syzygy with the C-syzygy of a module as well as the relation between the …

For a given class of modules A, let A˜ be the class of exact complexes having all cycles in A,
and dw (A) the class of complexes with all components in A. Denote by GI the class of …

We prove that if the ring R is left noetherian andif the class of Gorenstein injective modules,
GI, is closed under ltrations, then GI is precovering. We extend this result to the category of …

Let R be a commutative Noetherian local ring. A finitely generated Gorenstein projective R-
module M is called IG-projective if there exists either an irreducible epimorphism P→ M or …

For any ring R and any positive integer n, we prove that a left R-module is a Gorenstein n-
syzygy if and only if it is an n-syzygy. Over a left and right Noetherian ring, we introduce the …

Enochs and Jenda gave some characterizations of Gorenstein injective and projective
complexes over n-Gorenstein rings. The aim of this article is to generalize these results and …