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 …

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 …

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 …

设A, B 是环, U 是(B, A)-双模, n, d 为非负整数, T=(A 0U B) 是形式三角矩阵环, 首先,
证明了M=(M 1 M 2) φ M 是n-表现左T-模当且仅当M 1 是n-表现左A-模, Coker φ M 是n-表现左B …

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 …

Let A and B be rings, U a (B, A)-bimodule and T= A 0 UB be a triangular matrix ring. We first
give an explicit description for Gorenstein injective T-modules over the triangular matrix ring …

设是形式三角矩阵环, 其中A, B 是环, U 是左B 右A 双模. 证明了若BU 的平坦维数有限, UA
平坦维数或内射维数有限, 则左是PGF 模当且仅当左A-模M 1 是PGF 模, 左B-模M 2/Im (φ M) …

Let $ T $ be a right exact functor from an abelian category $\mathscr {B} $ into another
abelian category $\mathscr {A} $. Then there exists an abelian category, named comma …

Let A and B be rings and U a (B, A)-bimodule. If BU is flat and UA is finitely generated
projective (resp., BU is finitely generated projective and UA is flat), then the characterizations …

The origin of Gorenstein homological algebra may date back to 1960s when Auslander and
Bridger introduced the concept of G-dimension for finitely generated modules over a …