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

2016/09/01 by Gergely Kiss, Kiss, Gergely, Gábor Somlai +1
Computer Science · Mathematics · #06F05 #20M99 #FOS: Mathematics #Functional Equations Stability Results #Group Theory (math.GR) #Nonlinear Differential Equations Analysis #Optimization and Variational Analysis #math.GR #msc:06F05 #msc:20M99

paper · pdf · doi:10.48550/arxiv.1609.00279

openalex publication_date 2016/09/01 · arxiv created 2017/10/16 · arxiv updated 2017/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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