Stability of Gorenstein objects in triangulated categories

Z Wang, C Liang - arXiv preprint arXiv:1409.7274, 2014 - arxiv.org
Let $\mathcal {C} $ be a triangulated category with a proper class $\xi $ of triangles.
Asadollahi and Salarian introduced and studied $\xi $-Gorenstein projective and $\xi …

Gorenstein right derived functors of−⊗− with respect to semidualizing modules

J Hu, D Zhang, N Ding - Communications in Algebra, 2014 - Taylor & Francis
Full article: Gorenstein Right Derived Functors of − ⊗ −with Respect to Semidualizing
Modules Skip to Main Content Taylor and Francis Online homepage Taylor and Francis …

-Strongly Gorenstein Projective, Injective and Flat modules

G Zhao, Z Huang - arXiv preprint arXiv:0904.3045, 2009 - arxiv.org
In this paper, we study the relation between $ m $-strongly Gorenstein projective (resp.
injective) modules and $ n $-strongly Gorenstein projective (resp. injective) modules …

[HTML][HTML] Gorenstein triangular matrix rings and category algebras

R Wang - Journal of Pure and Applied Algebra, 2016 - Elsevier
We give conditions on when a triangular matrix ring is Gorenstein of a given selfinjective
dimension. We apply the result to the category algebra of a finite EI category. In particular …

[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 …

Gluing and lifting exact model structures for the recollement of exact categories

J Hu, H Zhu, R Zhu - arXiv preprint arXiv:2012.06067, 2020 - arxiv.org
In this paper, we first provide an explicit procedure to glue together hereditary exact model
structures for the recollement of exact categories. To that end, we use the notion of cotorsion …

[HTML][HTML] Gorenstein projective bimodules via monomorphism categories and filtration categories

W Hu, XH Luo, BL Xiong, G Zhou - Journal of Pure and Applied Algebra, 2019 - Elsevier
We generalize the monomorphism category from quiver (with monomial relations) to
arbitrary finite dimensional algebras by a homological definition. Given two finite dimension …

Ding modules and dimensions over formal triangular matrix rings

L Mao - arXiv preprint arXiv:1912.06968, 2019 - arxiv.org
Let $ T=\biggl (\begin {matrix} A&0\\U&B\end {matrix}\biggr) $ be a formal triangular matrix
ring, where $ A $ and $ B $ are rings and $ U $ is a $(B, A) $-bimodule. We prove that:(1) If …

[HTML][HTML] Gorenstein flat modules and dimensions over formal triangular matrix rings

L Mao - Journal of Pure and Applied Algebra, 2020 - Elsevier
Abstract Let T=(A 0 UB) be a formal triangular matrix ring, where A and B are rings and U is
a (B, A)-bimodule. We prove that, if T is a right coherent ring, UB has finite flat dimension, UA …

Gorenstein acyclic complexes and finitistic dimensions

L Shaul - arXiv preprint arXiv:2310.05247, 2023 - arxiv.org
Given a two-sided noetherian ring $ A $ with a dualizing complex, we show that the big
finitistic dimension of $ A $ is finite if and only if every bounded below Gorenstein-projective …