Taiwanese Journal of Mathematics

THE ASCENDING CHAIN CONDITION FOR PRINCIPAL LEFT IDEALS OF SKEW POLYNOMIAL RINGS

A. R. Nasr-Isfahani

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Abstract

In this note we study the ascending chain conditions on principal left (resp. right) ideals of the skew polynomial ring $R[x;\alpha,\delta]$. We give a characterization of skew polynomial rings $R[x;\alpha,\delta]$ that are domains and satisfy the ascending chain condition on principal left (resp. right) ideals. We also prove that if $R$ is an $\alpha$-rigid ring that satisfies the ascending chain condition on right annihilators and ascending chain condition on principal right (resp. left) ideals, then the skew polynomial ring $R[x;\alpha,\delta]$ and skew power series ring $R[[x;\alpha]]$ also satisfy the ascending chain condition on principal right (resp. left) ideals.

Article information

Source
Taiwanese J. Math., Volume 18, Number 3 (2014), 931-941.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499706450

Digital Object Identifier
doi:10.11650/tjm.18.2014.1663

Mathematical Reviews number (MathSciNet)
MR3213396

Zentralblatt MATH identifier
1357.16043

Subjects
Primary: 16P99: None of the above, but in this section 16S36: Ordinary and skew polynomial rings and semigroup rings [See also 20M25]

Keywords
skew polynomial ring skew power series ring ascending chain conditions on principal left (resp. right) ideals

Citation

Nasr-Isfahani, A. R. THE ASCENDING CHAIN CONDITION FOR PRINCIPAL LEFT IDEALS OF SKEW POLYNOMIAL RINGS. Taiwanese J. Math. 18 (2014), no. 3, 931--941. doi:10.11650/tjm.18.2014.1663. https://projecteuclid.org/euclid.twjm/1499706450


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