ON GORENSTEIN HOMOLOGICAL DIMENSIONS OF GROUPS
Received:February 21, 2022  Revised:July 30, 2022
Key Words: Gorenstein homological dimension   Serre's theorem   Group ring  
Fund Project:the Natural Science Foundation of Hunan Province (No.2021JJ30536)
Author NameAffiliationAddress
xiang yueming Huaihua university 怀化学院数学与计算科学学院
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Abstract:
      Let k be a commutative ring with fi nite weak dimension and let G be a group. In this paper, we explore the criterion that a group G has finite Gorenstein homological dimension. It is shown that the finiteness of the Gorenstein homological dimension of G coincides with the fi niteness of the Gorenstein weak dimension of the group ring kG. Furthermore, we give a Gorenstein analogy of the Serre's theorem. Some well-known results for the Gorenstein homological dimension of G over the integer ring are also extended.
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