ON REGULAR PARAMEDIAL DIVISION ALGEBRAS

Authors

  • David N. Harutyunyan Chair of Algebra and Geometry, YSU, Armenia

DOI:

https://doi.org/10.46991/PYSU:A/2022.56.3.107

Keywords:

hyperidentities, regular division groupoids, paramedial groupoids, n-ary groupoids, quasiendomorphisms

Abstract

In this paper $n$-ary regular division algebras are discussed, which are  satisfying the hyperidentity of paramediality. It is shown that every operation  in $n$-ary regular paramedial division algebra will be linearly represented over the same Abelian group. Similar results already obtained for regular medial division algebras in [1].

References

Davidov S.S. On Regular Medial Division Algebras. Quasigr. Relat. Syst. 21 (2013), 155--164.

Movsisyan Yu. Hyperidentities: Boolean and De Morgan Structures. World Scientific (2022), 560 p. https://doi.org/10.1142/12796

Movsisyan Yu. Introduction to the Theory of Algebras with Hyperidentities. Yerevan, YSU Press (1986) (in Russian).

Movsisyan Yu. Hyperidentities and Hypervarieties in Algebras. Yerevan, YSU Press (1990) (in Russian).

Ehsani A., Movsisyan Yu. A Representation of Paramedial $n$-ary Groupoids. Asian-Eur. J. Math. 7 (2014), 1450020. https://doi.org/10.1142/S179355711450020X

Davidov S. On Paramedial Division Groupoids. Asian-Eur. J. Math. 9 (2016), 1650008. https://doi.org/10.1142/S179355711650008X

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Published

2022-10-21

How to Cite

Harutyunyan, D. N. (2022). ON REGULAR PARAMEDIAL DIVISION ALGEBRAS. Proceedings of the YSU A: Physical and Mathematical Sciences, 56(3 (259), 107–115. https://doi.org/10.46991/PYSU:A/2022.56.3.107

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Section

Mathematics