CUBO A Mathematical Journal Vol.14, N° 01, (49-54). March 2012

Units in Abelian Group Algebras Over Direct Products of Indecomposable Rings

Peter Danchev

13, General Kutuzov Str. 4003 Plovdiv, Bulgaria, email: pvdanchev@yahoo.com

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 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).

Keywords and Phrases: groups, rings, group rings, indecomposable rings, units, direct decompositions, isomorphisms.

RESUMEN

Sea R un anillo conmutativo y unitario de característica prima p, que es producto directo de subanillos indescomponibles y sea G un grupo multiplicativo y abeliano tal que G₀/G_pp es finito. Caracterizamos las clases de isomorfismo del grupo unitario U(RG) del álgebra del grupo RG. Estos fuertes y recientes resultados se deben a Mollov-Nachev (Commun. Algebra, 2006) and Danchev (Studia Babes Bolyai - Mat., 2011).

2010 AMS Mathematics Subject Classification: 16S34, 16U60, 20K21.

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Received: October 2010. Revised: March 2011.