Document Type: Original Manuscript

Authors

1 Department of Mathematics, Gonbad Kavous University, P.O. Box 4971799151, Gonbad Kavous, Iran.

2 Department of Mathematics, University of Isfahan, P.O. Box: 81746-73441, Isfa- han, Iran.

Abstract

Let $(R, \m)$ be a commutative noetherian local ring and let $\Gamma$ be a finite group.
It is proved that if $R$ admits a dualizing module, then the group ring $R\ga$ has a
dualizing bimodule as well. Moreover, it is shown that a finitely generated $R\ga$-module $M$ has generalized
Gorenstein dimension zero if and only if it has generalized Gorenstein dimension zero
as an $R$-module.

Keywords