2018/08/14 by Matthew Moore, Moore, Matthew, Andrew Moorhead +1 · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Logic #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1808.04858
openalex publication_date 2018/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.