Let RM be a trivial extension of a ring R by an RR-bimodule M. Sufficient and necessary
conditions are established for Gorenstein flat-cotorsion modules over R M. More precisely, it …

In this paper, we introduce the notion of Gorenstein $(m, n) $-flat modules as an extension of
$(m, n) $-flat left $ R $-modules over a ring $ R $, where $ m $ and $ n $ are two fixed …

Let A and B be rings and U be a (B, A)-bimodule. If BU has finite flat dimension, UA has finite
flat dimension and U⊗ AC is a cotorsion left B-module for any cotorsion left A-module C …

Abstract Let R⊂ S be a Frobenius extension of rings and M a left S-module and let 𝓧 be a
class of left R-modules and 𝒚 a class of left S-modules. Under some conditions it is proven …

In this paper, Gorenstein FP-injective modules are introduced and studied. An R-module M
is called Gorenstein FP-injective if there is an exact sequence⋯→ E1→ E0→ E0→ E1→⋯ of …

By investigating the properties of some special covers and envelopes of modules, we prove
that if R is a Gorenstein ring with the injective envelope of RR flat, then a left R-module is …

Let R be a ring and let 𝒮𝒢ℱ be the class of strongly Gorenstein at right R-modules. We call a
right R-module M a weak Gorenstein cotorsion module if M is in the class 𝒮𝒢ℱ⊥. Properties …

In this paper, we introduce the concept of Gorenstein flat comodules and give a description
of colocalization of Gorenstein flat comodules. A right C-comodule M is called a Gorenstein …

A complex (C, δ) is called strongly Gorenstein flat if C is exact and Ker δ n is Gorenstein flat
in R-Mod for all n∈ ℤ. Let 𝒮𝒢 stand for the class of strongly Gorenstein flat complexes. We …

We introduce the concepts of generalized compatible and cocompatible bimodules in order
to characterize Gorenstein projective, injective and flat modules over trivial ring extensions …