We compare relative cohomology theories arising from using different proper resolutions of
modules. Criteria for the vanishing of such distinctions are given in certain cases, and we …

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 …

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 …

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 categories, J …