Gorenstein homological dimensions of modules over triangular matrix rings

Authors: RONGMIN ZHU, ZHONGKUI LIU, ZHANPING WANG

Abstract: Let $A$ and $B$ be rings, $U$ a $(B, A)$-bimodule, and $T=\left(\begin{smallmatrix} A & 0 \\ U & B \\\end{smallmatrix}\right)$ the triangular matrix ring. In this paper, we characterize the Gorenstein homological dimensions of modules over $T$, and discuss when a left $T$-module is a strongly Gorenstein projective or strongly Gorenstein injective module.

Keywords: Triangular matrix ring, Gorenstein regular ring, Gorenstein homological dimension

Full Text: PDF