[en] We investigate n-ary semigroups as a natural generalization of binary
semigroups. We refer it as a pair (X,F_n), where X is a set and an n-associative function
F_n : X^n -> X is defined on X. We show that if F_n is idempotent, n-associative
function which is monotone in each of its variables, defined on an interval I and has a neutral element, then F_n is combination of the minimum and maximum
operation. Moreover we can characterize the n-ary semigroups (I,F_n) where F_n has
the previous properties.
Disciplines :
Mathematics
Author, co-author :
Kiss, Gergely ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Somlai, Gabor
External co-authors :
no
Language :
English
Title :
Generalization of Czoga\l a-Drewniak Theorem for $n$-ary semigroups
