@Article{JMS-55-4,
author = {Wang, Jie and Xu, Xiaowei and Zhibing, Zhao},
title = {$\mathfrak{X}$-Gorenstein Projective Dimensions},
journal = {Journal of Mathematical Study},
year = {2022},
volume = {55},
number = {4},
pages = {398--414},
abstract = {<p style="text-align: justify;">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&#39;s theorem on the global dimension and its Gorenstein homological version.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v55n4.22.04},
url = {https://global-sci.com/article/87662/mathfrakx-gorenstein-projective-dimensions}
}