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 …
How to construct Gorenstein projective modules relative to complete duality pairs over Morita rings
Y Ma, J Lü, H Li, J Hu - arXiv preprint arXiv:2203.08673, 2022 - arxiv.org
Let $\Delta=\left (\begin {smallmatrix} A & {_AN_B}\\{_BM_A} & B\\\end {smallmatrix}\right) $
be a Morita ring with $ M\otimes_ {A} N= 0= N\otimes_ {B} M $. We first study how to …
be a Morita ring with $ M\otimes_ {A} N= 0= N\otimes_ {B} M $. We first study how to …
Special precovering classes in comma categories
J Hu, H Zhu - Science China Mathematics, 2022 - Springer
Let T be a right exact functor from an abelian category ℬ into another abelian category A.
Then there exists a functor p from the product category A× ℬ to the comma category ((T↓ …
Then there exists a functor p from the product category A× ℬ to the comma category ((T↓ …
Homological dimensions of special modules over formal triangular matrix rings
L Mao - Journal of Algebra and Its Applications, 2022 - World Scientific
Homological dimensions of special modules over formal triangular matrix rings Page 1 2 April 22,
2021 11:52 WSPC/S0219-4988 171-JAA 2250146 Journal of Algebra and Its Applications (2022) …
2021 11:52 WSPC/S0219-4988 171-JAA 2250146 Journal of Algebra and Its Applications (2022) …
Silting and cosilting modules over trivial ring extensions
L Mao - Communications in Algebra, 2022 - Taylor & Francis
We establish connections between (co, weak) silting modules over a ring R and (co, weak)
silting modules over a trivial extension of R. As applications, we describe how to construct …
silting modules over a trivial extension of R. As applications, we describe how to construct …
[HTML][HTML] Relative Gorenstein dimensions over triangular matrix rings
Let A and B be rings, U a (B, A)-bimodule, and T= A 0 UB the triangular matrix ring. In this
paper, several notions in relative Gorenstein algebra over a triangular matrix ring are …
paper, several notions in relative Gorenstein algebra over a triangular matrix ring are …
The Recollements of Abelian Categories: Cotorsion Dimensions and Cotorsion Triples
X Fu, Y Hu - Bulletin of the Iranian Mathematical Society, 2022 - Springer
In this paper, we study the cotorsion dimensions and cotorsion triples in the recollements of
abelian categories. The main results are that recollements induce new (resp. complete …
abelian categories. The main results are that recollements induce new (resp. complete …
Silting objects and torsion pairs in comma categories
P Zhang, M Chen, D Liu - arXiv preprint arXiv:2207.04437, 2022 - arxiv.org
In this paper, we first give a characterization of silting objects in the comma category Assume
that C1 and C2 are two subcategories of left R-modules, D1 and D2 be two subcategories of …
that C1 and C2 are two subcategories of left R-modules, D1 and D2 be two subcategories of …
Gorenstein flat-cotorsion modules over formal triangular matrix rings
D Wu - Bulletin of the Korean Mathematical Society, 2021 - koreascience.or.kr
Let A and B be rings and U be a (B, A)-bimodule. If BU has finite flat dimension, UA has finite
flat dimension and U⊗ AC is a cotorsion left B-module for any cotorsion left A-module C …
flat dimension and U⊗ AC is a cotorsion left B-module for any cotorsion left A-module C …
形式三角矩阵环上的余挠三元组
曹家乐， 杨晓燕 - Pure Mathematics, 2022 - hanspub.org
本文研究了形式三角矩阵环上的余挠三元组的问题. 设是形式三角矩阵环, 其中A 和B 是环, U
是左B-右A-双模. 本文利用A-模上完备(完全) 遗传的余挠三元组(C 1, C 2, C 3) 和B …
是左B-右A-双模. 本文利用A-模上完备(完全) 遗传的余挠三元组(C 1, C 2, C 3) 和B …