It is now well known that the conditions used by Auslander to define the Gorenstein
projective modules on Noetherian rings are independent. Recently, Ringel and Zhang …

We prove that for a left and right Noetherian ring $ R $, $ _RR $ satisfies the Auslander
condition if and only if so does every flat left $ R $-module, if and only if the injective …

In this paper, we study Gorenstein injective modules over a local Noetherian ring R. For an
R-module M, we show that M is Gorenstein injective if and only if Hom R (Ȓ, M) belongs to …

Let R be a commutative Noetherian ring. In this article, we provide some new criteria for a
semidualizing module to be dualizing in terms of special homological properties of module …

Let R be a commutative Noetherian ring and C a semidualizing R-module. We obtain an
exact structure (ℋ C, 𝜀) and prove that the full subcategory ℋ C∩ 𝒢 ℱ C of ℋ C is a …

The aim of this paper is to characterize $ n $-Gorenstein rings in terms of Gorenstein
injective modules and the Ext functor. We will show that if $ R $ is a left and right noetherian …

This paper generalize the idea of the authors in J. Pure Appl. Algebra 210 (2007) 437–445.
Namely, we define and study a particular case of Gorenstein projective modules. We …

We obtain some methods to construct a (strongly) proper resolution (resp. coproper
coresolution) of one end term in a short exact sequence from that of the other two terms. By …

Let R be a commutative Noetherian ring. In this paper, we study those finitely generated R-
modules whose Cousin complexes provide Gorenstein injective resolutions. We call such a …

This paper introduces and studies (X, Y)-Gorenstein projective and injective modules, which
are a generalization of Enochs' Gorenstein projective and injective modules, respectively …