Geodesic
On regular paramedial division algebras
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 56 (2022) no. 3, pp. 107-115 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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, $n$-ary groupoids, quasiendomorphisms.
Mots-clés : paramedial groupoids 
@article{UZERU_2022_56_3_a2,
     author = {D. N. Harutyunyan},
     title = {On regular paramedial division algebras},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {107--115},
     year = {2022},
     volume = {56},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZERU_2022_56_3_a2/}
}
TY  - JOUR
AU  - D. N. Harutyunyan
TI  - On regular paramedial division algebras
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 2022
SP  - 107
EP  - 115
VL  - 56
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/UZERU_2022_56_3_a2/
LA  - en
ID  - UZERU_2022_56_3_a2
ER  - 
%0 Journal Article
%A D. N. Harutyunyan
%T On regular paramedial division algebras
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 2022
%P 107-115
%V 56
%N 3
%U http://geodesic.mathdoc.fr/item/UZERU_2022_56_3_a2/
%G en
%F UZERU_2022_56_3_a2
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