Year: 2022
Author: Jie Wang, Xiaowei Xu, Zhibing Zhao
Journal of Mathematical Study, Vol. 55 (2022), Iss. 4 : pp. 398–414
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 a 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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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v55n4.22.04
Journal of Mathematical Study, Vol. 55 (2022), Iss. 4 : pp. 398–414
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Gorenstein projective modules $\mathfrak{X}$-Gorenstein projective modules $\mathfrak{X}$-Gorenstein projective dimensions the Auslander’s theorem.