Geodesic
Medial strong dependance $n$-ary operations
Diskretnaya Matematika, Tome 32 (2020) no. 2, pp. 112-121.

Voir la notice de l'article provenant de la source Math-Net.Ru

The article contains an extension of Toyoda–Belousov theorem describing medial $n$-ary qasigroups to strong dependance $n$-ary operations.
Keywords: $n$-ary quasigroup, strong dependance operation, medial operation. 
@article{DM_2020_32_2_a7,
     author = {A. V. Cheremushkin},
     title = {Medial strong dependance $n$-ary operations},
     journal = {Diskretnaya Matematika},
     pages = {112--121},
     publisher = {mathdoc},
     volume = {32},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2020_32_2_a7/}
}
TY  - JOUR
AU  - A. V. Cheremushkin
TI  - Medial strong dependance $n$-ary operations
JO  - Diskretnaya Matematika
PY  - 2020
SP  - 112
EP  - 121
VL  - 32
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2020_32_2_a7/
LA  - ru
ID  - DM_2020_32_2_a7
ER  - 
%0 Journal Article
%A A. V. Cheremushkin
%T Medial strong dependance $n$-ary operations
%J Diskretnaya Matematika
%D 2020
%P 112-121
%V 32
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2020_32_2_a7/
%G ru
%F DM_2020_32_2_a7
A. V. Cheremushkin. Medial strong dependance $n$-ary operations. Diskretnaya Matematika, Tome 32 (2020) no. 2, pp. 112-121. http://geodesic.mathdoc.fr/item/DM_2020_32_2_a7/

[1] Cheremushkin A. V., “Analogues of Gluskin–Hosszü and Malyshev theorems for strongly dependent n-ary operations”, Discrete Math. Appl., 29:5 (2019), 295–302 | DOI

[2] Cheremushkin A. V., “Teorema Posta dlya silno zavisimykh $n$-arnykh polugrupp”, Diskretnaya matematika, 31:2 (2019), 152–157

[3] Cheremushkin A. V., “Partially invertible strongly dependent $n$-ary operations”, Sb. Math., 211:2 (2020), 291–308 | DOI

[4] Toyoda K., “On axioms of linear functions”, Proc. Imp. Acad. Tokyo, 17 (1941), 221–227

[5] Bruck R. H., “Some results in the theory of quasigroups”, Trans. Amer. Math. Soc., 55 (1944), 19–52

[6] Belousov V. D., $n$-arnye kvazigruppy, Shtiintsa, Kishinev, 1972, 277 pp.

[7] Davidov S. S. On regular medial division algebras, Quasigroups and Related Systems, 21 (2013), 155–164

[8] Evans T., “Abstract mean values”, Duke Math. J., 30 (1963), 331–347

[9] Kepka T., “Medial division groupoids”, Acta Univ. Carolinae, Math. Phis., 20 (1979), 41–60

[10] Davidov S. S., “On the structure of medial divisible n-ary groupoids”, Math. Notes, 104:1 (2018), 29–38 | DOI

[11] Davidov S. S., “On the solvability of the equational theory of commutative medial n-ary groupoids”, Discrete Math. Appl., 23:2 (2013), 125–143 | DOI

[12] Davidov S. S., “Free commutative medial $n$-ary groupoids”, Discrete Math. Appl., 25:4 (2015), 203–210 | DOI

[13] Sokhatskii F. N., “Obobschenie dvukh teorem Belousova dlya silno zavisimykh funktsii $k$-znachnoi logiki”, Issledovaniya po teorii binarnykh i $n$-arnykh kvazigrupp. Matematicheskie issledovaniya, no. 85, Shtiintsa, Kishinev, 1985, 105–115

[14] Cheremushkin A. V., “Iteration-free decomposition of strongly dependent functions”, Discrete Math. Appl., 14:5 (2004), 439–478 | DOI