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arXiv · 1307.0628

Global dimensions of rings with respect to a semidualizing module

Guoqiang Zhao·Juxiang Sun
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Abstract

In this paper, the notion of strongly G_C-projective and injective modules is introduced, where C is a semidualizing module. Using these modules we can obtain a new characterization of G_C-projective and injective modules, similar to the one of projective modules by the free modules. We then define and study the global dimensions of rings relative to a semidualizing module C, and prove that the global G_C-projective dimension of a ring R is equal to the global G_C-injective dimension of R.

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Guoqiang Zhao, Juxiang Sun. 2013-07-02. Global dimensions of rings with respect to a semidualizing module. https://arxiv.org/abs/1307.0628

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