Polynomial rings over NLI rings need not be NLI

Weixing Chen

doi:10.1556/sscmath.52.2015.1.1305

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Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 52: Issue 1

Polynomial rings over NLI rings need not be NLI

Author:

Weixing Chen

Weixing Chen Shandong Institute of Business and Technology School of Mathematics and Information Science Yantai 264005 China

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Pages:: 129–133

Online Publication Date:: 17 Mar 2015

Publication Date:: 01 Mar 2015

Article Category:: Journal Article

DOI:: https://doi.org/10.1556/sscmath.52.2015.1.1305

Keywords:: Primary 16A30; 16A50; 16E50; 16D30; polynomial rings; Jacobson radicals; Koethe’s problem

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It is proved that there exists an NI ring R over which the polynomial ring R[x] is not an NLI ring. This answers an open question of Qu and Wei (Stud. Sci. Math. Hung., 51(2), 2014) in the negative. Moreover a sufficient condition of R[x] to be an NLI ring is included for an NLI ring R.

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Studia Scientiarum Mathematicarum Hungarica

Print ISSN:: 0081-6906

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Studia Scientiarum Mathematicarum Hungarica
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