Bimodule resolution of a group algebra

The authors investigate relations of the bimodule resolution of the group algebra of a finite group $G$ over a commutative ring with an usual projective resolution of the trivial $G$-module. In particular, the analogue of Happel's lemma is proved; this lemma was established earlier for finite dimensional algebras over fields. As an example of application of results, the bimodule resolution is constructed for the integer group ring of the dihedral group of order $4m$. Bibl. – 10 titles.