One of the open problems in Gorenstein homological algebra is: when is the class of
Gorenstein injective modules closed under arbitrary direct limits? It is known that if the class …

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 …

Over a commutative Noetherian ring R, the Bass invariants μi (p, M) were defined for any
module M and any prime p∈ Spec R by H. Bass (Math. Z. 82, 1963, 8-28). In the first part of …

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 …

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 …

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 generalize the idea of the authors in\cite {Bennis and Mahdou1}. Namely, we
define and study a particular case of modules with Gorenstein projective, injective, and flat …

Reiten has demonstrated that the trivial Hochschild extension of a Cohen-Macaulay local
ring by a canonical module is a Gorenstein local ring. Here it is proved that any commutative …

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