Gorenstein homological dimensions of modules over triangular matrix rings

Abstract

Let $A$ and $B$ be rings, $U$ a $(B,A)$-bimodule and $T=\left(\begin{array}{cc}A& 0\\ U& B\end{array}\right)$ be 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 strongly Gorenstein projective or strongly Gorenstein injective module.

14 pages