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 …

Auslander's depth formula for pairs of Tor-independent modules over a regular local ring,
depth (M⊗ RN)= depth M+ depth N− depth R, has been generalized in several directions; …

For finitely generated modules M and N over a Gorenstein local ring R, one has depth M+
depth N= depth (M⊗ RN)+ depth R, ie, the depth formula holds, if M and N are Tor …

We introduce Tate homology of complexes of finite Gorenstein flat dimension based on
complete flat resolutions and give a new method of computing Tate homology in …

In this paper, we are concerned with Tate homology tor ̂ tor of modules of finite Gorenstein
FI-flat dimension. We determine connections between Tate, relative and absolute homology …

We introduce and investigate Tate homology \rmtor of modules of finite Gorenstein flat
dimension. In particular, we show that over a right coherent ring R, \rmtor_i^R(M,N)≅ …

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 …

In this article we give a sufficient condition of the existence of 𝕎 t-approximation
presentations. We also introduce property (W k). As an application of the existence of 𝕎 t …

The depth formula for modules with reducible complexity Page 1 Illinois Journal of Mathematics
Volume 55, Number 2, Summer 2011, Pages 465–478 S 0019-2082 THE DEPTH FORMULA …

Relative homology and the structure of relative approximations Page 1 Vol. 45 No. 7 SCIENCE
IN CHINA (Series A) July 2002 Relative homology and the structure of relative approximations …