Generalization of Czogała-Drewniak Theorem for n-ary Semigroups
نویسندگان
چکیده
We investigate n-ary semigroups as a natural generalization of binary semigroups. We refer it as a pair (X ,Fn), where X is a set and an n-associative function Fn : Xn → 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 ⊂ 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.
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تاریخ انتشار 2017