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 …
Relative homological dimensions and Tate cohomology of complexes with respect to cotorsion pairs
X Yang, W Chen - Communications in Algebra, 2017 - Taylor & Francis
Let (𝒳, 𝒴) be a complete and hereditary cotorsion pair in a bicomplete abelian category 𝒜.
We introduce a Gorenstein category 𝒢 (𝒳) and 𝒢 (𝒳)-resolution dimension of complexes …
We introduce a Gorenstein category 𝒢 (𝒳) and 𝒢 (𝒳)-resolution dimension of complexes …
Tate cohomology for complexes with finite Gorenstein AC-injective dimension
J Xing, T Zhao, Y Li, J Hu - Bulletin of the Iranian Mathematical Society, 2019 - Springer
In this paper, we introduce and study a notion of Gorenstein AC-injective dimension for
complexes of left modules over associative rings. We show first that the class of complexes …
complexes of left modules over associative rings. We show first that the class of complexes …
[HTML][HTML] Triangulated equivalence between a homotopy category and a triangulated quotient category
Z Di, Z Liu, X Yang, X Zhang - Journal of Algebra, 2018 - Elsevier
Given two complete hereditary cotorsion pairs (Q, R) and (Q′, R′) in a bicomplete abelian
category G such that Q′⊆ Q and Q∩ R= Q′∩ R′, Becker showed that there exists a …
category G such that Q′⊆ Q and Q∩ R= Q′∩ R′, Becker showed that there exists a …
Relative singularity categories with respect to Gorenstein flat modules
ZX Di, ZK Liu, XX Zhang - Acta Mathematica Sinica, English Series, 2017 - Springer
Let R be a right coherent ring and D b (R-Mod) the bounded derived category of left R-
modules. Denote by D^ b\left (R-Mod\right) _\left GF, C\right D b (R− M od) GF, C^ the …
modules. Denote by D^ b\left (R-Mod\right) _\left GF, C\right D b (R− M od) GF, C^ the …
Buchweitz's equivalences for Gorenstein flat modules with respect to semidualizing modules
J Hu, Y Geng, J Wu, H Li - Journal of Algebra and Its Applications, 2021 - World Scientific
Let R be a commutative Noetherian ring and C a semidualizing R-module. We obtain an
exact structure (ℋ C, 𝜀) and prove that the full subcategory ℋ C∩ 𝒢 ℱ C of ℋ C is a …
exact structure (ℋ C, 𝜀) and prove that the full subcategory ℋ C∩ 𝒢 ℱ C of ℋ C is a …
[PDF][PDF] Relative cohomology dimensions of complexes based on degreewise cotorsion pairs
Z Liu, J LI, Z Wang - PUBLICATIONES MATHEMATICAE …, 2022 - researchgate.net
Let R be an associative ring with identity, and (A, B) a hereditary cotorsion pair generated by
a set in R-Mod. Then (dw A,(dw A)⊥) is a complete and hereditary cotorsion pair (we call it …
a set in R-Mod. Then (dw A,(dw A)⊥) is a complete and hereditary cotorsion pair (we call it …
Complete cohomology for complexes with finite Gorenstein AC-projective dimension
J Hu, Y Geng, Q Jiang - Frontiers of Mathematics in China, 2016 - Springer
We study complete cohomology of complexes with finite Gorenstein AC-projective
dimension. We show first that the class of complexes admitting a complete level resolution is …
dimension. We show first that the class of complexes admitting a complete level resolution is …
Tate-Vogel and relative cohomologies of complexes with respect to cotorsion pairs
J Hu, H Li, J Wei, X Yang, N Ding - arXiv preprint arXiv:1707.02678, 2017 - arxiv.org
We study Tate-Vogel and relative cohomologies of complexes by applying the model
structure induced by a complete hereditary cotorsion pair ($\A $, $\B $) of modules. We show …
structure induced by a complete hereditary cotorsion pair ($\A $, $\B $) of modules. We show …
[引用][C] Gorenstein -flat dimension of complexes and relative singularity categories
W Chen - Journal of Algebra and Its Applications, 2023 - World Scientific
Assume that the class of all Gorenstein (ℒ, 𝒜)-flat modules is closed under extensions. We
define a notion of Gorenstein (ℒ, 𝒜)-flat dimension for complexes and consider equivalent …
define a notion of Gorenstein (ℒ, 𝒜)-flat dimension for complexes and consider equivalent …