Gorenstein homological dimensions of modules over triangular matrix rings

Authors : Rongmin ZHU, Zhongkui LIU, Zhanping WANG

Pages : 146-160

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :Let $A$ and $B$ be rings, $U$ a $insert ignore into journalissuearticles values(B, A);$-bimodule, and $T=\leftinsert ignore into journalissuearticles values(\begin{smallmatrix} A & 0 \\ U & B \\\end{smallmatrix}\right);$ 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