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arXiv · 1801.09127

$\mathfrak{X}$-Gorenstein projective dimensions

Zhibing Zhao·Xiaowei Xu
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Abstract

In this paper, we mainly investigate the $\mathfrak{X}$-Gorenstein projective dimension of modules and the (left) $\mathfrak{X}$-Gorenstein global dimension of rings. Some properties of $\mathfrak{X}$-Gorenstein projective dimensions are obtained. Furthermore, we prove that the (left) $\mathfrak{X}$-Gorenstein global dimension of ring $R$ is equal to the supremum of the set of $\mathfrak{X}$-Gorenstein projective dimensions of all cyclic (left) $R$-modules. This result extends the well-known Auslander's theorem on the global dimension and its Gorenstein homological version.

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Zhibing Zhao, Xiaowei Xu. 2018-01-27. $\mathfrak{X}$-Gorenstein projective dimensions. https://arxiv.org/abs/1801.09127

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