Units in Abelian Group Algebras Over Direct Products of Indecomposable Rings

Peter Danchev

doi:10.4067/S0719-06462012000100005

Units in Abelian Group Algebras Over Direct Products of Indecomposable Rings

Authors

Peter Danchev General Kutuzov Str. 4003 Plovdiv, Bulgaria.

DOI:

https://doi.org/10.4067/S0719-06462012000100005

Keywords:

groups, rings, group rings, indecomposable rings, units, direct decompositions, isomorphisms

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).