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COMPLETELY PRIME ONE-SIDED IDEALS IN SKEW POLYNOMIAL RINGS

Part of: Modules, bimodules and ideals Conditions on elements Rings and algebras arising under various constructions

Published online by Cambridge University Press:  03 February 2021

GIL ALON  and
ELAD PARAN
GIL ALON
Affiliation:
The Open University of Israel, Ra’anana 4353701, Israel, e-mails: gilal@openu.ac.il, paran@openu.ac.il
ELAD PARAN
Affiliation:
The Open University of Israel, Ra’anana 4353701, Israel, e-mails: gilal@openu.ac.il, paran@openu.ac.il
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Abstract

Let R = K[x, σ] be the skew polynomial ring over a field K, where σ is an automorphism of K of finite order. We show that prime elements in R correspond to completely prime one-sided ideals – a notion introduced by Reyes in 2010. This extends the natural correspondence between prime elements and prime ideals in commutative polynomial rings.

MSC classification

Primary: 16D25: Ideals 16U20: Ore rings, multiplicative sets, Ore localization 16U30: Divisibility, noncommutative UFDs 16U80: Generalizations of commutativity
Secondary: 16S32: Rings of differential operators
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 64 , Issue 1 , January 2022 , pp. 114 - 121
Copyright
© The Author(s) 2021. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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