Generalization of Czogala-Drewniak Theorem for n-ary Semigroups

摘要

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 Fn is idempotent, n-associative function which is monotone in each of its variables, defined on an interval I C R and has a neutral element, then Fn is combination of the minimum and maximum operation. Moreover we can characterize the n-ary semigroups (I, Fn) where Fn has the previous properties.