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http://hdl.handle.net/10662/15350
| Títulos: | Trivial units in commutative group algebras |
| Autores/as: | Danchev, Peter |
| Palabras clave: | Unidades normadas;Unidades triviales;Anillos de grupo;Anillos indescomponibles;Anillos reducidos;Idempotentes;Nilpotentes |
| Fecha de publicación: | 2008 |
| Editor/a: | Universidad de Extremadura, Servicio de Publicaciones |
| Resumen: | Let 𝐺 be an arbitrary abelian group and let 𝑅 be a commutative unitary ring of arbitrary characteristic. A necessary and su±cient condition is given for when all units in the group ring 𝑅𝐺 are trivial provided that either supp(𝐺) ∩ inv(𝑅) ≠∅ ; or 𝑅𝐺 is modular. In particular, we establish a comprehensive characterization by finding a criterion when 𝑅𝐺 has only trivial units provided that char(𝑅) is a positive number greater than 1. These achievements strengthen results due to Karpilovsky (Arch. Math. Basel, 1983), Herman-Li Parmenter (Can. Math. Bull., 2005) and the author (Math. Commun., 2005). |
| URI: | http://hdl.handle.net/10662/15350 |
| ISSN: | 0213-8743 |
| Colección: | Extracta Mathematicae Vol. 23, nº 1 (2008) |
Archivos
| Archivo | Descripción | Tamaño | Formato | |
|---|---|---|---|---|
| 2605-5686_23_1_49.pdf | 167,32 kB | Adobe PDF | Descargar |
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