Relative Gorenstein rings and duality pairs

J Wang, Z Di - Journal of Algebra and Its Applications, 2020 - World Scientific
Let R be a ring (not necessarily commutative) and (ℒ, 𝒜) a bi-complete duality pair. We
investigate the notions of (flat-typed)(ℒ, 𝒜)-Gorenstein rings, which unify Iwanaga …

Model structures, recollements and duality pairs

W Chen, Z Liu - Journal of Algebra and Its Applications, 2023 - World Scientific
In this paper, we construct some model structures corresponding Gorenstein (ℒ, 𝒜)-modules
and relative Gorenstein flat modules associated to duality pairs, Frobenius pairs and …

Gorenstein and duality pair over triangular matrix rings

H Liu, R Zhu - arXiv preprint arXiv:2202.13148, 2022 - arxiv.org
Let $ A $, $ B $ be two rings and $ T=\left (\begin {smallmatrix} A & M\\0 & B\\\end
{smallmatrix}\right) $ with $ M $ an $ A $-$ B $-bimodule. We first construct a semi-complete …

AC-Gorenstein rings and their stable module categories

J Gillespie - Journal of the Australian Mathematical Society, 2019 - cambridge.org
We introduce what is meant by an AC-Gorenstein ring. It is a generalized notion of
Gorenstein ring that is compatible with the Gorenstein AC-injective and Gorenstein AC …

[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 …

Model structures on categories of complexes over Ding-Chen rings

G Yang, Z Liu, L Liang - Communications in Algebra, 2013 - Taylor & Francis
The so-called Ding–Chen ring is an n-FC ring which is both left and right coherent, and has
both left and right self FP-injecitve dimensions at most n for some non-negative integer n. In …

Homotopy equivalences induced by balanced pairs

XW Chen - Journal of Algebra, 2010 - Elsevier
We introduce the notion of balanced pair of additive subcategories in an abelian category.
We give sufficient conditions under which a balanced pair of subcategories gives rise to a …

Gorenstein AC-projective complexes

J Gillespie - Journal of Homotopy and Related Structures, 2018 - Springer
Let R be any ring with identity and Ch (R) C h (R) the category of chain complexes of (left) R-
modules. We show that the Gorenstein AC-projective chain complexes of 1 are the cofibrant …

Triangulated equivalences involving Gorenstein projective modules

Y Zheng, Z Huang - Canadian Mathematical Bulletin, 2017 - cambridge.org
For any ring R, we show that, in the bounded derived category Db (Mod R) of le R-modules,
the subcategory of complexes with nite Gorenstein projective (resp. injective) dimension …

[引用][C] Generalized Gorenstein modules with respect to duality pairs over triangular matrix rings

R Zhu, H Liu - International Journal of Algebra and Computation, 2024 - World Scientific
Let A and B be rings and T=(AM 0 B) with M an AB-bimodule. We first construct a semi-
complete duality pair DT of over T using duality pairs over A and B respectively. Then we …