A characterization of $n$-associative, monotone, idempotent functions on an interval that have neutral elements

Gergely Kiss; Gábor Somlai

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arXiv · 1609.00279

A characterization of $n$-associative, monotone, idempotent functions on an interval that have neutral elements

Gergely Kiss·Gábor Somlai

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Abstract

We investigate monotone idempotent $n$-ary semigroups. One of the main result of this article is the generalisation of Czogala-Drewniak Theorem, which describes the idempotent monotone associative functions having neutral element. Furthermore we present the full characterisation of idempotent, monotone, $n$-associative functions on an interval which have neutral elements. %{\bl defined}. Our description provides that monotone, idempotent, $n$-ary semigroups are quasitrivial.

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Gergely Kiss, Gábor Somlai. 2017-10-16. A characterization of $n$-associative, monotone, idempotent functions on an interval that have neutral elements. https://arxiv.org/abs/1609.00279

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