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 |
| _version_ | 1818260169343107072 |
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| author | Peter Danchev |
| author_facet | Peter Danchev |
| author_sort | Peter Danchev |
| collection | DOAJ |
| description | 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). |
| first_indexed | 2024-12-12T18:27:04Z |
| format | Article |
| id | doaj.art-dfd2a888fe4a45869a8d890361975dce |
| institution | Directory Open Access Journal |
| issn | 0716-7776 0719-0646 |
| language | English |
| last_indexed | 2024-12-12T18:27:04Z |
| publishDate | 2012-01-01 |
| publisher | Universidad de La Frontera |
| record_format | Article |
| series | Cubo |
| spelling | doaj.art-dfd2a888fe4a45869a8d890361975dce2022-12-22T00:16:00ZengUniversidad de La FronteraCubo0716-77760719-06462012-01-011414954Units in Abelian Group Algebras Over Direct Products of Indecomposable RingsPeter DanchevLet 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).http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462012000100005groupsringsgroup ringsindecomposable ringsunitsdirect decompositionsisomorphisms |
| spellingShingle | Peter Danchev Units in Abelian Group Algebras Over Direct Products of Indecomposable Rings Cubo groups rings group rings indecomposable rings units direct decompositions isomorphisms |
| title | Units in Abelian Group Algebras Over Direct Products of Indecomposable Rings |
| title_full | Units in Abelian Group Algebras Over Direct Products of Indecomposable Rings |
| title_fullStr | Units in Abelian Group Algebras Over Direct Products of Indecomposable Rings |
| title_full_unstemmed | Units in Abelian Group Algebras Over Direct Products of Indecomposable Rings |
| title_short | Units in Abelian Group Algebras Over Direct Products of Indecomposable Rings |
| title_sort | units in abelian group algebras over direct products of indecomposable rings |
| topic | groups rings group rings indecomposable rings units direct decompositions isomorphisms |
| url | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462012000100005 |
| work_keys_str_mv | AT peterdanchev unitsinabeliangroupalgebrasoverdirectproductsofindecomposablerings |