Geodesic
On regular paramedial division algebras
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 56 (2022) no. 3, pp. 107-115.

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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].
Keywords: hyperidentities, regular division groupoids, paramedial groupoids, $n$-ary groupoids, quasiendomorphisms. 
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D. N. Harutyunyan. On regular paramedial division algebras. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 56 (2022) no. 3, pp. 107-115. http://geodesic.mathdoc.fr/item/UZERU_2022_56_3_a2/

[1] S. S. Davidov, “Regular Medial Division Algebras”, Quasigroups and Related Systems, 21 (2013), 155–164 | MR | Zbl

[2] Yu. M. Movsisyan, Hyperidentities: Boolean and De Morgan Structures, World Scientific, 2022, 560 pp. | DOI | Zbl

[3] Yu. M. Movsisyan, Introduction to the Theory of Algebras with Hyperidentities, YSU Press, Yerevan, 1986 (in Russian) | MR

[4] Yu. M. Movsisyan, Hyperidentities and Hypervarieties in Algebras, YSU Press, Yerevan, 1990 (in Russian) | MR

[5] A. Ehsan, Yu. M. Movsisyan, “A Representation of Paramedial $n$-ary Groupoids”, Asian-Eur. J. Math., 7 (2014), 1450020 | DOI | MR | Zbl

[6] S. Davidov, “On Paramedial Division Groupoids”, Asian-Eur. J. Math., 9:1 (2016), 1650008 | DOI | MR | Zbl