Czechoslovak Mathematical Journal, Vol. 71, No. 3, pp. 803-816, 2021
Weak dimensions and Gorenstein weak dimensions of group rings
Yueming Xiang
Received March 6, 2020. Published online March 22, 2021.
Abstract: Let $K$ be a field, and let $G$ be a group. In the present paper, we investigate when the group ring $K[G]$ has finite weak dimension and finite Gorenstein weak dimension. We give some analogous versions of Serre's theorem for the weak dimension and the Gorenstein weak dimension.
Keywords: weak dimension; Gorenstein weak dimension; principal module; group ring
Affiliations: Yueming Xiang, School of Mathematics and Computational Science, Huaihua University, Huaihua, 418000, P. R. China, e-mail: xymls999@126.com