A refinement of Gorenstein flat dimension via the flat–cotorsion theory
We introduce a refinement of the Gorenstein flat dimension for complexes over an
associative ring—the Gorenstein flat-cotorsion dimension—and prove that it, unlike the …
associative ring—the Gorenstein flat-cotorsion dimension—and prove that it, unlike the …
Gorenstein dimensions of unbounded complexes and change of base (with an appendix by Driss Bennis)
LW Christensen, F Köksal, L Liang - Science China Mathematics, 2017 - Springer
For a commutative ring R and a faithfully flat R-algebra S we prove, under mild extra
assumptions, that an R-module M is Gorenstein flat if and only if the left S-module S⊗ RM is …
assumptions, that an R-module M is Gorenstein flat if and only if the left S-module S⊗ RM is …
On Gorenstein global and Gorenstein weak global dimensions
J Wang, G Yang, Q Shao, X Zhang - Colloquium Mathematicum, 2023 - impan.pl
It is well-known that the weak global dimension of a ring does not exceed its global
dimension. Christensen et al. obtained a corresponding result in Gorenstein setting for …
dimension. Christensen et al. obtained a corresponding result in Gorenstein setting for …
Stable homology over associative rings
O Celikbas, L Christensen, L Liang… - Transactions of the …, 2017 - ams.org
Accepted Manuscript Page 1 Olgur Celikbas, Lars Winther Christensen, Li Liang, Greg
Piepmeyer Stable homology over associative rings Transactions of the American …
Piepmeyer Stable homology over associative rings Transactions of the American …
Homology theories for complexes based on flats
L Liang - Glasgow Mathematical Journal, 2021 - cambridge.org
In this paper, we introduce and study the Gorenstein relative homology theory for
unbounded complexes of modules over arbitrary associative rings, which is defined using …
unbounded complexes of modules over arbitrary associative rings, which is defined using …
Homology theories and Gorenstein dimensions for complexes
L Liang - Algebras and Representation Theory, 2021 - Springer
In this paper, we first study the Gorenstein projective/flat dimension of complexes of
modules. The relation between the Gorenstein projective/flat dimension for complexes and …
modules. The relation between the Gorenstein projective/flat dimension for complexes and …
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 …
相对于半对偶模的Gorenstein 平坦维数有限的模的Tate 同调
潘晓玲, 梁力 - 《 山东大学学报(理学版)》, 2019 - lxbwk.njournal.sdu.edu.cn
相对于半对偶模的Gorenstein平坦维数有限的模的Tate同调 Page 1 山东大学学报(理学版)2019年
12月第54卷第12期 E-mail:xblxb@sdu.edu.cn Journal of Shandong University (Natural …
12月第54卷第12期 E-mail:xblxb@sdu.edu.cn Journal of Shandong University (Natural …
[PDF][PDF] Stable homology
O Celikbas, LW Christensen, L Liang… - arXiv preprint arXiv …, 2014 - Citeseer
We analyze stable homology over associative rings and obtain results over Artin algebras
and commutative noetherian rings. Our study develops similarly for these classes; for …
and commutative noetherian rings. Our study develops similarly for these classes; for …
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 …