Enveloping algebras that are principal ideal rings

Let L be a restricted Lie algebra over a field of positive characteristic. We prove that the restricted enveloping algebra of L is a principal ideal ring if and only if L is an extension of a finite-dimensional torus by a cyclic restricted Lie algebra.

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Bibliographic Details
Published in:Journal of pure and applied algebra 2017-10, Vol.221 (10), p.2573-2581
Main Authors: Siciliano, Salvatore, Usefi, Hamid
Format: Article
Language:English
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Summary:Let L be a restricted Lie algebra over a field of positive characteristic. We prove that the restricted enveloping algebra of L is a principal ideal ring if and only if L is an extension of a finite-dimensional torus by a cyclic restricted Lie algebra.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2017.01.003