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Medientyp:
E-Artikel
Titel:
The equation solvability problem over supernilpotent algebras with Mal’cev term
Beteiligte:
Kompatscher, Michael
Erschienen:
World Scientific Pub Co Pte Lt, 2018
Erschienen in:International Journal of Algebra and Computation
Sprache:
Englisch
DOI:
10.1142/s0218196718500443
ISSN:
0218-1967;
1793-6500
Entstehung:
Anmerkungen:
Beschreibung:
<jats:p> In 2011, Horváth gave a new proof that the equation solvability problem over finite nilpotent groups and rings is in P. In the same paper, he asked whether his proof can be lifted to nilpotent algebras in general. We show that this is in fact possible for supernilpotent algebras with a Mal’cev term. However, we also describe a class of nilpotent, but not supernilpotent algebras with Mal’cev term that have co-NP-complete identity checking problems and NP-complete equation solvability problems. This proves that the answer to Horváth’s question is negative in general (assuming P[Formula: see text]NP). </jats:p>