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 …
[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 …
Triangle equivalences involving Gorenstein FP-injective modules
Z Di, X Zhang, Z Liu - Communications in Algebra, 2018 - Taylor & Francis
Recently, Hu et al. introduced the notion of Gorenstein FP-injective modules and
investigated a notion of Gorenstein FP-injective dimension for complexes. Let R be a left …
investigated a notion of Gorenstein FP-injective dimension for complexes. Let R be a left …
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 …
Stability of Gorenstein flat categories
G Yang, Z Liu - Glasgow Mathematical Journal, 2012 - cambridge.org
A left R-module M is called two-degree Gorenstein flat if there exists an exact sequence of
Gorenstein flat left R-modules⋅⋅⋅→ G2→ G1→ G0→ G− 1→ G− 2→⋅⋅⋅ such that M≅ Ker …
Gorenstein flat left R-modules⋅⋅⋅→ G2→ G1→ G0→ G− 1→ G− 2→⋅⋅⋅ such that M≅ Ker …
[PDF][PDF] Model structures, n-Gorenstein flat modules and PGF dimensions
R El Maaouy - arXiv e-prints, 2023 - researchgate.net
Given a non-negative integer n and a ring R with identity, we construct a hereditary abelian
model structure on the category of left R-modules where the class of cofibrant objects …
model structure on the category of left R-modules where the class of cofibrant objects …
[HTML][HTML] The flat stable module category of a coherent ring
J Gillespie - Journal of Pure and Applied Algebra, 2017 - Elsevier
Let R by a right coherent ring and R-Mod denote the category of left R-modules. We show
that there is an abelian model structure on R-Mod whose cofibrant objects are precisely the …
that there is an abelian model structure on R-Mod whose cofibrant objects are precisely the …
Stability of Gorenstein flat categories with respect to a semidualizing module
Z Di, Z Liu, J Chen - 2015 - projecteuclid.org
We first introduce in the paper the W_F-Gorenstein modules to establish the following Foxby
equivalence: \xymatrix@C=80ptG(F)∩A_C\ar@\lt0.5ex>r^C⊗_R-\amp\,\,\,\,G(W_F)\ar@\lt0 …
equivalence: \xymatrix@C=80ptG(F)∩A_C\ar@\lt0.5ex>r^C⊗_R-\amp\,\,\,\,G(W_F)\ar@\lt0 …
Gorenstein flat modules relative to injectively resolving subcategories
Z Gao, W Wu - Journal of Algebra and Its Applications, 2022 - World Scientific
Let ℰ be an injectively resolving subcategory of left R-modules. We introduce and study ℰ-
Gorenstein flat modules as a common generalization of some known modules such as …
Gorenstein flat modules as a common generalization of some known modules such as …
[HTML][HTML] Relative singularity categories, Gorenstein objects and silting theory
J Wei - Journal of Pure and Applied Algebra, 2018 - Elsevier
We study singularity categories through Gorenstein objects in triangulated categories and
silting theory. Let ω be a presilting subcategory of a triangulated category T. We introduce …
silting theory. Let ω be a presilting subcategory of a triangulated category T. We introduce …