2018/01/27 by Zhibing Zhao, Zhao, Zhibing, Xiao-Wei Xu +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1801.09127
openalex publication_date 2018/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we mainly investigate the \mathfrakX-Gorenstein projective dimension of modules and the (left) \mathfrakX-Gorenstein global dimension of rings. Some properties of \mathfrakX-Gorenstein projective dimensions are obtained. Furthermore, we prove that the (left) \mathfrakX-Gorenstein global dimension of ring R is equal to the supremum of the set of \mathfrakX-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.