About ternary quasigroup quadratic identities of the small length
In this article, it has been proved that each quadratic identity of the lengths one, two, three is parastrophically primarily equivalent to at least one of the given identities. The identities of the length three have been analyzed in the class of universal loops, i.e., quasigroups in which every el...
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| Datum: | 2020 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine
2020
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| Schlagworte: | |
| Online Zugang: | http://journals.iapmm.lviv.ua/ojs/index.php/APMM/article/view/apmm2020.18.150-161 |
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| Назва журналу: | Prykladni Problemy Mekhaniky i Matematyky |
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Prykladni Problemy Mekhaniky i Matematyky| Zusammenfassung: | In this article, it has been proved that each quadratic identity of the lengths one, two, three is parastrophically primarily equivalent to at least one of the given identities. The identities of the length three have been analyzed in the class of universal loops, i.e., quasigroups in which every element is neutral. It has been proved that there are five non-equivalent identities. The first identity defines the class of all universal loops, the second one defines the variety of the boolean skeins and the other three identities define three parastrophic varieties whose operations are repetition-free compositions of binary commutative middle loops. Cite as: F. M. Sokhatsky, A. V. Tarasevych, “On ternary quasigroup quadratic identities of the small length,” Prykl. Probl. Mekh. Mat., Issue 18, 150–161 (2020), https://doi.org/10.15407/apmm2020.18.150-161 |
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