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.
Citation
A. R. Nasr-Isfahani. "THE ASCENDING CHAIN CONDITION FOR PRINCIPAL LEFT IDEALS OF SKEW POLYNOMIAL RINGS." Taiwanese J. Math. 18 (3) 931 - 941, 2014. https://doi.org/10.11650/tjm.18.2014.1663
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