Units in Abelian Group Algebras Over Direct Products of Indecomposable Rings

Abstract

Let R be a commutative unitary ring of prime characteristic p which is a direct product of indecomposable subrings and let G be a multiplicative Abelian group such that G₀/G_p is finite. We characterize the isomorphism class of the unit group U(RG) of the group algebra RG. This strengthens recent results due to Mollov-Nachev (Commun. Algebra, 2006) and Danchev (Studia Babes Bolyai - Mat., 2011).