Abdolnaser Bahlekeh - Department of Mathematics, Gonbad Kavous University, P.O. Box ۴۹۷۱۷۹۹۱۵۱, Gonbad Kavous, Iran.
T. Kakaie - Department of Mathematics, University of Isfahan, P.O. Box: ۸۱۷۴۶-۷۳۴۴۱, Isfa- han, Iran.

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 $Rga$ has a dualizing bimodule as well. Moreover, it is shown that a finitely generated $Rga$-module $M$ has generalized Gorenstein dimension zero if and only if it has generalized Gorenstein dimension zero as an $R$-module.

Semi-dualizing bimodules, generalized Gorenstein dimension, group rings