Open Access
2009 Duo, Bézout, and Distributive Rings of Skew Power Series
Ryszard Mazurek, Michał Ziembowski
Publ. Mat. 53(2): 257-271 (2009).


We give necessary and sufficient conditions on a ring $R$ and an endomorphism $\sigma$ of $R$ for the skew power series ring $R[[x; \sigma]]$ to be right duo right Bézout. In particular, we prove that $R[[x; \sigma]]$ is right duo right Bézout if and only if $R[[x; \sigma]]$ is reduced right distributive if and only if $R[[x; \sigma]]$ is right duo of weak dimension less than or equal to $1$ if and only if $R$ is $\aleph_0$-injective strongly regular and $\sigma$ is bijective and idempotent-stabilizing, extending to skew power series rings the Brewer-Rutter-Watkins characterization of commutative Bézout power series rings.


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Ryszard Mazurek. Michał Ziembowski. "Duo, Bézout, and Distributive Rings of Skew Power Series." Publ. Mat. 53 (2) 257 - 271, 2009.


Published: 2009
First available in Project Euclid: 20 July 2009

zbMATH: 1176.16034
MathSciNet: MR2543853

Primary: 16W60
Secondary: 16D50 , 16E50

Keywords: right Bézout ring , right distributive ring , right duo ring , Skew power series ring

Rights: Copyright © 2009 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.53 • No. 2 • 2009
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