Let R be a ring. For two fixed positive integers m and n, a right R-module M is called (m, n)-
injective in case every right R-homomorphism from an n-generated submodule of Rm to M …

In this paper, we introduce the concepts of Gorenstein FI-injective and Gorenstein FI-flat
modules and we are concerned with the stability of the class of Gorenstein FI-flat modules …

Abstract A left R-module M is said to be fp-injective if, for every monomorphism K→ L with K
and L finitely presented left R-modules, Hom (L, M)→ Hom (K, M) is an epimorphism. A right …

Abstract The so-called Ding-Chen ring is an n-FC ring which is both left and right coherent,
and has both left and right self FP-injective dimensions at most n for some non-negative …

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 …

We extend the notion of virtually Gorenstein rings to the setting of arbitrary rings, and prove
that all rings R of finite Gorenstein weak global dimension are virtually Gorenstein such that …

The concept of Gorenstein dimension, defined by Auslander and Bridger for finitely
generated modules over a Noetherian ring, is studied in the context of finitely presented …

In this paper, we construct some non-integrally closed domains in Gorenstein multiplicative
ideal theory. For example, we show that there exists a Gorenstein Prüfer domain which is …

A ring is left Gorenstein regular if the classes of left modules with finite projective dimension
and finite injective dimension coincide and the injective and projective finitistic left …

We introduce the notion of totally reflexive extension of rings. It unifies Gorenstein orders
and Frobenius extensions. We prove that for a totally reflexive extension, a module over the …