## On a decomposition of normalized units in Abelian group algebras.(English)Zbl 1165.16017

Let $$G$$ be an Abelian group and $$R$$ a commutative ring with identity of prime characteristic $$p$$. Let $$V(RG)$$ be the normalized unit group of the group ring $$RG$$, and let $$S(RG)$$ be the $$p$$-component of torsion of $$RG$$. The author explicitly finds necessary and sufficient conditions such that $$V(RG)=GS(RG)$$. This extends the author’s previous result [in An. Univ. Bucur., Mat. 54, No. 2, 229-234 (2005; Zbl 1137.16306)] where a field $$F$$ of characteristic $$p$$ was used instead of a commutative ring with identity.

### MSC:

 16U60 Units, groups of units (associative rings and algebras) 16S34 Group rings 20C07 Group rings of infinite groups and their modules (group-theoretic aspects)

Zbl 1137.16306