An n-FC ring is a left and right coherent ring whose left and right self-FP-injective dimension
is n. The work of Ding and Chen shows that these rings possess properties which generalize …

We introduce and investigate Tate homology \rmtor of modules of finite Gorenstein flat
dimension. In particular, we show that over a right coherent ring R, \rmtor_i^R(M,N)≅ …

Let A be an abelian category. For a pair (X, Y) of classes of objects in A, we define the weak
and the (X, Y)-Gorenstein relative projective objects in A. We point out that such objects …

In this article, we give a new characterization of Gorenstein projective modules. As
applications of our result, we prove that a strongly Gorenstein projective module of …

The purpose of this paper is to give, via totally different techniques, an alternate proof to the
main theorem of [18] in the category of modules over an arbitrary ring R. In effect, we prove …

Duality properties are studied for a Gorenstein algebra that is finite and projective over its
center. Using the homotopy category of injective modules, it is proved that there is a local …

Let be a class of left R-modules that contains all projective left R-modules. We study a kind
of stability of-Gorenstein projective modules and settle in affirmative the following question …

We give necessary and sufficient conditions in order for the class of projectively coresolved
Gorenstein flat modules, PGF (respectively that of projectively coresolved Gorenstein B flat …

One of the main results of this paper is the characterization of the rings over which all
modules are strongly Gorenstein projective. We show that these kinds of rings are very …

Starting from the notion of totally reflexive modules, we survey the theory of Gorenstein
homological dimensions for modules over commutative rings. The account includes the …