(untitled) (Journal of Mathematical Study, 2022)
In this paper, we mainly investigate the X-Gorenstein projective dimension of modules and the (left) X-Gorenstein global dimension of rings. Some properties of X-Gorenstein projective dimensions are obtained. Furthermore, we prove that the (left) X-Gorenstein global dimension of a ring R is equal to the supremum of the set of 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.