Units in Abelian Group Algebras Over Direct Products of Indecomposable Rings

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/gp is nite. 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).