In this paper, we introduce and study relative Auslander--Gorenstein pairs. This consists of a
finite-dimensional Gorenstein algebra together with a self-orthogonal module that provides a …

Let R be an artin algebra. We prove that a tilting R-module ω is cotilting if and only if every
finitely generated R-module has finite ω-Gorenstein resolution dimension and that a cotilting …

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 article, the new concept of relative Gorenstein flat modules is introduced. We give a
survey of their behavior in terms of both structural and dimension properties. We relate the …

Relative cotilting modules and their connection to ordinary cotilting modules were first
studied by Auslander and Solberg in [6] and [7]. Among other things, they show that relative …

Let R and S be rings, and let R ω S be a semidualizing bimodule. We prove that there exists
a Morita equivalence between the class of∞-ω-cotorsion-free modules and a subclass of the …

Inspired in part by recent work of\v {S} aroch and\v {S}\v {t} ov\'{\i}\v {c} ek in the setting of
Gorenstein homological algebra, we extend the notion of Foxby-Golod ${\rm G_C} …

Given a complete hereditary cotorsion pair-Gorenstein projective modules and study its
stability properties. As applications, we first get two model structures related to 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 …

The monomorphism category S n (X) is introduced, where X is a full subcategory of the
module category A-mod of an Artin algebra A. The key result is a reciprocity of the …