## Kyoto Journal of Mathematics

### Virtual Gorensteinness over group algebras

#### Abstract

Let $\Gamma$ be a finite group, and let $\Lambda$ be any Artin algebra. It is shown that the group algebra $\Lambda\Gamma$ is virtually Gorenstein if and only if $\Lambda\Gamma '$ is virtually Gorenstein, for all elementary abelian subgroups $\Gamma '$ of $\Gamma$. We also extend this result to cover the more general context. Precisely, assume that $\Gamma$ is a group in Kropholler’s hierarchy $\mathbf{H}\mathfrak{F}$, $\Gamma '$ is a subgroup of $\Gamma$ of finite index, and $R$ is any ring with identity. It is proved that, in certain circumstances, that $R\Gamma$ is virtually Gorenstein if and only if $R\Gamma '$ is so.

#### Article information

Source
Kyoto J. Math., Volume 55, Number 1 (2015), 129-141.

Dates
First available in Project Euclid: 13 March 2015

https://projecteuclid.org/euclid.kjm/1426252132

Digital Object Identifier
doi:10.1215/21562261-2848133

Mathematical Reviews number (MathSciNet)
MR3323529

Zentralblatt MATH identifier
1329.16010

#### Citation

Bahlekeh, Abdolnaser; Salarian, Shokrollah. Virtual Gorensteinness over group algebras. Kyoto J. Math. 55 (2015), no. 1, 129--141. doi:10.1215/21562261-2848133. https://projecteuclid.org/euclid.kjm/1426252132

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