The equation solvability problem over supernilpotent algebras with Mal'cev term

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10383441" target="_blank" >RIV/00216208:11320/18:10383441 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1142/S0218196718500443" target="_blank" >https://doi.org/10.1142/S0218196718500443</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S0218196718500443" target="_blank" >10.1142/S0218196718500443</a>

Result language
angličtina
Original language name
The equation solvability problem over supernilpotent algebras with Mal'cev term
Original language description
In 2011, Horvath 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 Horvath's question is negative in general (assuming P not equal NP).
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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