Group Rings of Finite Gorenstein Homological Dimensions

EasyChair Preprint no. 11284

Abstract

Let K be a eld and let G be a group. In the study of group ring K[G], there is the well-known Serre's theorem which consider the niteness of global dimension of group ring. In the present paper, we investigate when the group ring K[G] has nite Gorenstein global dimension. It is shown that the Gorenstein global dimension of K[G] shares many properties with the global dimension of K[G].  Finally, we give some analogous versions of the Serre’s Theorem for Gorenstein global dimension.

Keyphrases: (Gorenstein) global dimensions, group rings, principal modules

@Booklet{EasyChair:11284,
  author = {Xiang Yueming},
  title = {Group Rings of Finite Gorenstein Homological Dimensions},
  howpublished = {EasyChair Preprint no. 11284},

  year = {EasyChair, 2023}}