Supernilpotence need not imply nilpotence

JOURNAL OF ALGEBRA

卷:535

Article

Moore, Matthew¹  Moorhead, Andrew² 

[1] Univ Kansas, Dept Elect Engn & Comp Sci, Eaton Hall, Lawrence, KS 66044 USA

[2] Vanderbilt Univ, Dept Math, Nashville, TN 37235 USA

关键词: Commutator theory;    Higher commutator theory;    Supernilpotent algebras;    Taylor variety;   

DOI  :  10.1016/j.jalgebra.2019.07.002

来源: Elsevier

【 摘 要 】

Supernilpotence is a generalization of nilpotence using a recently developed theory of higher-arity commutators for universal algebras. Many important structural properties have been shown to be associated with supernilpotence, and the exact relationship between nilpotence and supernilpotence has been the subject of investigation. We construct an algebra which is not solvable (and hence not nilpotent) but which is supernilpotent, thereby showing that in general supernilpotence does not imply nilpotence. We also extend this construction to 'higher dimensions' to obtain similar results for (n)-step supernilpotence. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free