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 …

We introduce and investigate in this paper a kind of Tate homology of modules over a
commutative coherent ring based on Tate ℱC-resolutions, where C is a semidualizing …

We compare and contrast various relative cohomology theories that arise from resolutions
involving semidualizing modules. We prove a general balance result for relative …

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 …

Let R be a commutative Cohen–Macaulay ring, and let C be a semidualizing module of R. In
this paper, we show that C is generically dualizing if and only if the tensor products of …

Let $(R,\fm) $ be a local ring and $ C $ be a homologically bounded and finitely generated $
R $-complex. Then, we prove that $ C $ is a dualizing complex of $ R $ if and only if $ C $ is …

We provide a general method to construct the Tate–Vogel homology theory for a general
half-exact functor with one variable, aiming at a good generalization of Cohen–Macaulay …

Let S and R be two associative rings, SCR be a faithfully balanced (S, R)-bimodule. We
introduce and investigate properties of∞-torsionfree modules with respect to SCR, which …

Given two complete hereditary cotorsion pairs (𝒬, ℛ) and (𝒬′, ℛ′) in the category of
modules which satisfy the conditions 𝒬′⊆ 𝒬, 𝒬∩ ℛ= 𝒬′∩ ℛ′, and ℛ′ is enveloping, a …

We investigate stable homology of modules over a commutative noetherian ring R with
respect to a semidualzing module C, and give some vanishing results that improve/extend …