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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)

Citations:

Zbl 1137.16306
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