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 …

We study the Gorenstein weak global dimension of associative rings and its relation to the
Gorenstein global dimension. In particular, we prove the conjecture that the Gorenstein …

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 …

A ring R is called Gorenstein hereditary (G-hereditary) if every submodule of a projective
module is Gorenstein projective (ie Ggldim (R)≤ 1). In this paper, we settle a question …

We prove that any faithful Frobenius functor between abelian categories preserves the
Gorenstein projective dimension of objects. Consequently, it preserves and reflects …

On (Strongly) Gorenstein (Semi)Hereditary Rings Page 1 Arab J Sci Eng (2011) 36:431–440
DOI 10.1007/s13369-011-0047-7 RESEARCH ARTICLE - MATHEMATICS Najib Mahdou …

Abstract Let (C, E, s)(C, E, s) be an extriangulated category with a proper class ξ ξ of E E-
triangles. In a previous work, we introduced and studied the ξ ξ-GG projective and the ξ ξ-GG …

We present and study the concept of m-periodic Gorenstein objects relative to a pair (A, B) of
classes of objects in an abelian category, as a generalization of m-strongly Gorenstein …

In the last few years, López-Permouth and several collaborators have introduced a new
approach in the study of the classical projectivity, injectivity and flatness of modules. This …