Geodesic
Properties of strong dependance $n$-ary semigroups
Prikladnaya Diskretnaya Matematika. Supplement, no. 12 (2019), pp. 36-41

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

The paper presents results about the structure of strongly dependent $n$-ary operations on a finite set that satisfy the associativity identities for the $n$-ary semigroup, $n\ge 3$. It is shown that their description is reduced to the description of binary semigroups with a unit satisfying certain properties. The information is based on the proof of analogues of the Post and Gluskin–Hossu theorems for the case of strongly dependent operations. It is also proved that any strong dependence binary semigroup is a monoid. A description of autotopy groups of strongly dependent $n$-ary semigroup is also given.
Keywords: $n$-ary semigroup, strongly dependent function, autotopy group. 
@article{PDMA_2019_12_a9,
     author = {A. V. Cheremushkin},
     title = {Properties of strong dependance $n$-ary semigroups},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {36--41},
     publisher = {mathdoc},
     number = {12},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2019_12_a9/}
}
TY  - JOUR
AU  - A. V. Cheremushkin
TI  - Properties of strong dependance $n$-ary semigroups
JO  - Prikladnaya Diskretnaya Matematika. Supplement
PY  - 2019
SP  - 36
EP  - 41
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDMA_2019_12_a9/
LA  - ru
ID  - PDMA_2019_12_a9
ER  - 
%0 Journal Article
%A A. V. Cheremushkin
%T Properties of strong dependance $n$-ary semigroups
%J Prikladnaya Diskretnaya Matematika. Supplement
%D 2019
%P 36-41
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDMA_2019_12_a9/
%G ru
%F PDMA_2019_12_a9
A. V. Cheremushkin. Properties of strong dependance $n$-ary semigroups. Prikladnaya Diskretnaya Matematika. Supplement, no. 12 (2019), pp. 36-41. http://geodesic.mathdoc.fr/item/PDMA_2019_12_a9/