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 resul...
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| Format: | Article |
| Language: | English |
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Universidad de La Frontera
2012-01-01
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| Series: | Cubo |
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| Online Access: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462012000100005 |
| Summary: | 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).<br>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/Gp p 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). |
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| ISSN: | 0716-7776 0719-0646 |