Let R be a general ring. Duality pairs of R-modules were introduced by Holm-Jørgensen.
Most examples satisfy further properties making them what we call semi-complete duality …

We introduce a generalization of the Gorenstein injective modules: the Gorenstein FP n-
injective modules (denoted by GI n). They are the cycles of the exact complexes of injective …

We introduce the notion of a duality pair and demonstrate how the left half of such a pair is"
often" covering and preenveloping. As an application, we generalize a result by Enochs et …

Let R be a ring, C be a left R-module and S= End R (C). When C is semidualizing, the
Auslander class AC (S) and the Bass class ℬ C (R) associated with C have been the subject …

Let R be a commutative ring. We show that any complete duality pair gives rise to a theory of
relative homological algebra, analogous to Gorenstein homological algebra. Indeed …

We characterize Ding modules and complexes over Ding-Chen rings. We show that, over a
Ding-Chen ring R, the Ding projective (respectively, Ding injective, respectively, Ding flat) R …

Let R be any ring with identity and Ch (R) C h (R) the category of chain complexes of (left) R-
modules. We show that the Gorenstein AC-projective chain complexes of 1 are the cofibrant …

We prove that the class of Gorenstein injective modules is both enveloping and covering
over a two sided noetherian ring such that the character modules of Gorenstein injective …

Auslander and Solberg introduced the concepts of finitely generated cotilting and tilting
modules in relative homological algebra considering subfunctors of the Ext-functor. In this …

A semi-dualizing module over a commutative noetherian ring A is a finitely generated
module C with RHomA (C, C)≃ A in the derived category D (A). We show how each such …