Let C be a semidualizing R-module, where R is a commutative ring. We first introduce the
definition of C-cotorsion modules, and obtain the properties of C-cotorsion modules. As …

Let R be a ring. It is reasonable to use a strict 𝒲𝒳-resolution of a right R-module M of finite 𝒳-
projective dimension, where 𝒳 denotes a subcategory of right R-modules closed under …

The notion of relative derived category with respect to a subcategory is introduced. A triangle-
equivalence, which extends a theorem of Gao and Zhang [Gorenstein derived …

We derive in the paper the tensor product functor $-\otimes_R-$ by using proper $\mathcal
{G}\mathcal {P} _C $-resolutions, where $ C $ is a semidualizing module. After giving …

In this article, we study finite Gorenstein homological dimensions of complexes with respect
to a semidualizing module. A special attention is paid to the dimensions of homologically …

In this paper, for a fixed semidualizing module C, we introduce the notion of DC-projective
modules which are the special setting of GC-projective modules introduced by White [D …

Let C be a semidualizing R-module over a commutative coherent ring R. In this artical, we
show that if S is a faithfully flat commutative R-algebra such that the class of C⊗ R S …

This work studies the notions of k-torsionless modules and reduced G-perfect modules in a
more general setting, relative to a semidualizing module. We consider various aspects and …

In this paper we are concerned with absolute, relative and Tate Tor modules. In the first part
of the paper we generalize a result of Avramov and Martsinkovsky by using the Auslander …

Based on the analysis of Tate and generalized Tate cohomology in abelian categories, in
this note, we consider the balance for Tate and generalized Tate cohomology. Some …