Ding modules and dimensions over formal triangular matrix rings
نویسندگان
چکیده
Let $T=\bigl(\begin{smallmatrix}A&0\U\&B\end{smallmatrix}\bigr)$ be a formal triangular matrix ring, where $A$ and $B$ are rings $U$ is $(B, A)$-bimodule. We prove: (1) If $U\_{A}$ ${B}U$ have finite flat dimensions, then left $T$-module $\bigl(\begin{smallmatrix}M\_1\ M\_2\end{smallmatrix}\bigr){\varphi^{M}}$ Ding projective if only $M\_1$ $M\_2/{\operatorname{im}(\varphi^{M})}$ the morphism $\varphi^{M}$ monomorphism. (2) $T$ right coherent has dimension, $U{A}$ finitely presented or $\operatorname{FP}$-injective $(W\_1, W\_2){\varphi{W}}$ injective $W\_1$ $\ker(\widetilde{\varphi\_W})$ $\widetilde{\varphi\_W}$ an epimorphism. As consequence, we describe dimensions of $T$-module.
منابع مشابه
Zero-Divisor Graph of Triangular Matrix Rings over Commutative Rings
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ژورنال
عنوان ژورنال: Rendiconti del Seminario Matematico della Università di Padova
سال: 2022
ISSN: ['0041-8994', '2240-2926', '0373-319X']
DOI: https://doi.org/10.4171/rsmup/100