Open Access
April 2015 Virtual Gorensteinness over group algebras
Abdolnaser Bahlekeh, Shokrollah Salarian
Kyoto J. Math. 55(1): 129-141 (April 2015). DOI: 10.1215/21562261-2848133


Let Γ be a finite group, and let Λ be any Artin algebra. It is shown that the group algebra ΛΓ is virtually Gorenstein if and only if ΛΓ' is virtually Gorenstein, for all elementary abelian subgroups Γ' of Γ. We also extend this result to cover the more general context. Precisely, assume that Γ is a group in Kropholler’s hierarchy HF, Γ' is a subgroup of Γ of finite index, and R is any ring with identity. It is proved that, in certain circumstances, that RΓ is virtually Gorenstein if and only if RΓ' is so.


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Abdolnaser Bahlekeh. Shokrollah Salarian. "Virtual Gorensteinness over group algebras." Kyoto J. Math. 55 (1) 129 - 141, April 2015.


Published: April 2015
First available in Project Euclid: 13 March 2015

zbMATH: 1329.16010
MathSciNet: MR3323529
Digital Object Identifier: 10.1215/21562261-2848133

Primary: 13H10 , 16E65 , 16G10 , 20J05

Keywords: group algebras , Moore’s condition , virtually Gorenstein algebra

Rights: Copyright © 2015 Kyoto University

Vol.55 • No. 1 • April 2015
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