A study of Tate homology via the approximation theory with applications to the depth formula
O Celikbas, L Liang, A Sadeghi, T Sharif - Acta Mathematica Sinica …, 2023 - Springer
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 …
of the paper we generalize a result of Avramov and Martsinkovsky by using the Auslander …
[HTML][HTML] Vanishing of Tate homology and depth formulas over local rings
LW Christensen, DA Jorgensen - Journal of Pure and Applied Algebra, 2015 - Elsevier
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; …
depth (M⊗ RN)= depth M+ depth N− depth R, has been generalized in several directions; …
[HTML][HTML] Vanishing of relative homology and depth of tensor products
O Celikbas, L Liang, A Sadeghi - Journal of Algebra, 2017 - Elsevier
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 …
depth N= depth (M⊗ RN)+ depth R, ie, the depth formula holds, if M and N are Tor …
Complete flat resolutions, Tate homology and the depth formula
Y Liu, Z Liu, X Yang - Kodai Mathematical Journal, 2017 - jstage.jst.go.jp
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 …
complete flat resolutions and give a new method of computing Tate homology in …
Gorenstein FI-Flat Dimension and Tate Homology
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 …
FI-flat dimension. We determine connections between Tate, relative and absolute homology …
Tate homology of modules of finite Gorenstein flat dimension
L Liang - Algebras and Representation Theory, 2013 - Springer
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)≅ …
dimension. In particular, we show that over a right coherent ring R, \rmtor_i^R(M,N)≅ …
Tate homology with respect to cotorsion pairs
Z Di, Z Liu, X Zhang - Communications in Algebra, 2018 - Taylor & Francis
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 …
modules which satisfy the conditions 𝒬′⊆ 𝒬, 𝒬∩ ℛ= 𝒬′∩ ℛ′, and ℛ′ is enveloping, a …
Approximation presentations of modules and homological conjectures
Z Huang - Communications in Algebra®, 2008 - Taylor & Francis
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 …
presentations. We also introduce property (W k). As an application of the existence of 𝕎 t …
The depth formula for modules with reducible complexity
PA Bergh, DA Jorgensen - Illinois Journal of Mathematics, 2011 - projecteuclid.org
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 …
Volume 55, Number 2, Summer 2011, Pages 465–478 S 0019-2082 THE DEPTH FORMULA …
Relative homology and the structure of relative approximations
Z Huang - Science in China Series A: Mathematics, 2002 - Springer
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 …
IN CHINA (Series A) July 2002 Relative homology and the structure of relative approximations …