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arXiv · 1501.05410

Gorenstein (semi)hereditary rings with respect to a semidualizing module

Guoqiang Zhao·Juxiang Sun
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Abstract

Let $C$ be a semidualizing module. We first investigate the properties of finitely generated $G_C$-projective modules. Then, relative to $C$, we introduce and study the rings of Gorenstein (weak) global dimensions at most 1, which we call $C$-Gorenstein (semi)hereditary rings, and prove that every $C$-Gorenstein hereditary ring is both coherent and $C$-Gorenstein semihereditary.

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Guoqiang Zhao, Juxiang Sun. 2015-01-22. Gorenstein (semi)hereditary rings with respect to a semidualizing module. https://arxiv.org/abs/1501.05410

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