Let R be a Gorenstein ring. We first study Gorenstein orthogonal classes and Gorenstein
cotorsion pairs of R-modules. Then, we introduce the concept of Gorenstein weak tilting R …

In this paper, weak tilting modules are introduced and investigated. We show that all tilting
modules are weak tilting modules, but the converse is not true. We prove that a module is …

Let A/S be a ring extension with S commutative. We prove that ω⊗ S AA is a generalized
tilting module if ωS is a generalized tilting module. In this case, we obtain that⊥ ω-resol …

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 …

The theory of finitely generated relative (co) tilting modules has been established in the
1980s by Auslander and Solberg, and infinitely generated relative tilting modules have …

Let R be a ring. An R-module N is called Gorenstein cotorsion module if Ext R 1 (F, N)= 0 for
any Gorenstein flat R-module F. We investigate some properties of Gorenstein cotorsion …

We introduce the notion of ω-Gorenstein modules, where ω is a faithfully balanced self-
orthogonal module. This gives a common generalization of both Gorenstein projective …

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 T be a tilting module. In this paper, Gorenstein σ [T]-injective modules are introduced and
some of their basic properties are studied. Moreover, some characterizations of rings over …

In this paper, firstly, we characterize some rings by strict Mittag-Leffler conditions. Then, we
investigate when Gorenstein projective modules are Gorenstein flat by employing tilting …