Duo, Bézout and distributive rings of skew power series
We give necessary and sufficient conditions on a ring R and an endomorphism σ of R for the skew power series ring R[[x; σ]] to be right duo right Bézout. In particular, we prove that R[[x; σ]] is right duo right Bézout if and only if R[[x; σ]] is reduced right distributive if and only if R[[x; σ]] i...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2009 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:49668 |
| Acceso en línea: | https://ddd.uab.cat/record/49668 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_53209_01 |
| Access Level: | acceso abierto |
| Palabra clave: | Skew power series ring Rright Bézout ring Right distributive ring Right duo ring |
| Sumario: | We give necessary and sufficient conditions on a ring R and an endomorphism σ of R for the skew power series ring R[[x; σ]] to be right duo right Bézout. In particular, we prove that R[[x; σ]] is right duo right Bézout if and only if R[[x; σ]] is reduced right distributive if and only if R[[x; σ]] is right duo of weak dimension less than or equal to 1 if and only if R is N0-injective strongly regular and σ is bijective and idempotent-stabilizing, extending to skew power series rings the Brewer-Rutter-Watkins characterization of commutative B'ezout power series rings. |
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