A functional identity of generalized transitivity for strongly dependent $n$-ary operations
Diskretnaya Matematika, Tome 35 (2023) no. 4, pp. 146-156.

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

We proof that functional identity of generalized transitivity for strongly dependent operations may be described in analogy with quasigroups by replacing term «group» by term «monoid». We show how to generalize this result to $n$-ary strongly dependent operations.
Keywords: binary and $n$-ary quasigroups, strongly dependent operation, generalized transitivity identity.
@article{DM_2023_35_4_a9,
     author = {A. V. Cheremushkin},
     title = {A functional identity of generalized transitivity for strongly dependent $n$-ary operations},
     journal = {Diskretnaya Matematika},
     pages = {146--156},
     publisher = {mathdoc},
     volume = {35},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2023_35_4_a9/}
}
TY  - JOUR
AU  - A. V. Cheremushkin
TI  - A functional identity of generalized transitivity for strongly dependent $n$-ary operations
JO  - Diskretnaya Matematika
PY  - 2023
SP  - 146
EP  - 156
VL  - 35
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2023_35_4_a9/
LA  - ru
ID  - DM_2023_35_4_a9
ER  - 
%0 Journal Article
%A A. V. Cheremushkin
%T A functional identity of generalized transitivity for strongly dependent $n$-ary operations
%J Diskretnaya Matematika
%D 2023
%P 146-156
%V 35
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2023_35_4_a9/
%G ru
%F DM_2023_35_4_a9
A. V. Cheremushkin. A functional identity of generalized transitivity for strongly dependent $n$-ary operations. Diskretnaya Matematika, Tome 35 (2023) no. 4, pp. 146-156. http://geodesic.mathdoc.fr/item/DM_2023_35_4_a9/

[1] Cheremushkin A. V., “Analogi teorem Gluskina – Khossu i Malysheva dlya sluchaya silno zavisimykh $n$-arnykh operatsii”, Diskretnaya matematika, 30:2 (2018), 15–24 | DOI

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

[3] Cheremushkin A. V., “Chastichno obratimye silno zavisimye $n$-arnye operatsii”, Matematicheskii sbornik, 211:2 (2020), 141–158 | DOI | MR | Zbl

[4] Movsisyan Yu. M., “Biprimitivnye klassy algebr vtoroi stupeni”, Matem. issled., 9 (1974), 70–82 | MR | Zbl

[5] Krapez̆ A., “Functional equations of generalized associativity, bisymmetry, transitivity and distributivity”, Publ. Inst. Math., 30(44) (1981), 81–87 | MR | Zbl

[6] Movsisyan Yu. M., Davidov S. S., Algebry, blizkie k kvazigruppam, URSS, M., 2018, 407 pp.

[7] Belousov V. D., $n$-arnye kvazigruppy, Shtiintsa, Kishinev, 1972, 227 pp.

[8] Cheremushkin A. V., “Bespovtornaya dekompoziiya silno zavisimykh funktsii”, Diskretnaya matematika, 16:3 (2004), 3–42 | DOI | MR | Zbl