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...

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Detalles Bibliográficos
Autores: Mazurek, Ryszard, Ziembowski, Michal
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
Descripción
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.