Year: 2018
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Moore, Matthew, Moorhead, Andrew
Institutions: University of Kansas, Vanderbilt University
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Univerzita Karlova v Praze
OpenAlex ID: W2955478744