How to construct Gorenstein projective modules relative to complete duality pairs over Morita rings
Y Ma, J Lü, H Li, J Hu - Journal of Algebra and Its Applications, 2024 - World Scientific
Let Δ= AANBBMAB be a Morita ring with M⊗ AN= 0= N⊗ BM. We first study how to construct
(complete) duality pairs of Δ-modules using (complete) duality pairs of A-modules and B …
(complete) duality pairs of Δ-modules using (complete) duality pairs of A-modules and B …
[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 𝒟 T over T using duality pairs over A and B, respectively. Then we …
complete duality pair 𝒟 T over T using duality pairs over A and B, respectively. Then we …
Construction of Gorenstein-projective modules over Morita rings
D Asefa - Journal of Algebra and Its Applications, 2023 - World Scientific
In this paper, we obtain necessary and sufficient conditions for all complete projective
resolutions over a Morita ring Δ (0, 0)(A, B, M, N)= AANBBMAB. As special cases, we get a …
resolutions over a Morita ring Δ (0, 0)(A, B, M, N)= AANBBMAB. As special cases, we get a …
Strongly Gorenstein-projective modules over rings of Morita contexts
D Asefa - Beiträge zur Algebra und Geometrie/Contributions to …, 2024 - Springer
Abstract Let Δ (0, 0)= AANBBMAB be a Morita ring such that the bimodule homomorphisms
are zero. In this paper, we give sufficient conditions for a Δ (0, 0)-module (X, Y, f, g) to be …
are zero. In this paper, we give sufficient conditions for a Δ (0, 0)-module (X, Y, f, g) to be …
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 …
{smallmatrix}\right) $ with $ M $ an $ A $-$ B $-bimodule. We first construct a semi-complete …
Model structures and recollements induced by duality pairs
W Chen, L Li, Y Rao - arXiv preprint arXiv:2108.00140, 2021 - arxiv.org
We give some equivalent characterizations of $\mathcal {GP} $, the class of Gorenstein
$(\mathcal {L},\mathcal {A}) $-projective modules, and construct some model structures …
$(\mathcal {L},\mathcal {A}) $-projective modules, and construct some model structures …
Gorenstein projective, injective and flat modules over trivial ring extensions
L Mao - arXiv preprint arXiv:2305.15656, 2023 - arxiv.org
We introduce the concepts of generalized compatible and cocompatible bimodules in order
to characterize Gorenstein projective, injective and flat modules over trivial ring extensions …
to characterize Gorenstein projective, injective and flat modules over trivial ring extensions …
Gorenstein projective modules and recollements over triangular matrix rings
H Li, Y Zheng, J Hu, H Zhu - Communications in Algebra, 2020 - Taylor & Francis
Abstract Let T=(RM 0 S) be a triangular matrix ring with R and S rings and RMS an R–S-
bimodule. We describe Gorenstein projective modules over T. In particular, we refine a result …
bimodule. We describe Gorenstein projective modules over T. In particular, we refine a result …
[引用][C] Frobenius pairs arising from Morita rings
L Liang, Y Ma, G Yang - Journal of Algebra and Its Applications, 2024 - World Scientific
This paper is to study how to construct Frobenius pairs over a Morita ring Λ= AANBBMAB.
Given Frobenius pairs (X, W) and (Y, V) in AM od and BM od, respectively, we construct …
Given Frobenius pairs (X, W) and (Y, V) in AM od and BM od, respectively, we construct …
[引用][C] Strongly Gorenstein-injective modules over Morita rings
D Asefa - Journal of Algebra and Its Applications, 2023 - World Scientific
In this paper, we consider Morita rings with zero bimodule homomorphisms. We establish
necessary and sufficient conditions for all strongly complete injective resolutions over a …
necessary and sufficient conditions for all strongly complete injective resolutions over a …