A description of n-ary semigroups polynomial-derived from integral domains

TL;DR

This paper classifies n-ary semigroup structures derived from polynomial functions over infinite commutative integral domains, extending previous work on ternary semigroups to a more general setting.

Contribution

It provides a comprehensive classification of n-ary semigroups from polynomial functions over infinite integral domains, generalizing earlier ternary semigroup results.

Findings

Complete classification of n-ary semigroup structures

Extension of ternary semigroup classification to n-ary case

Generalization to infinite commutative integral domains

Abstract

We provide a complete classification of the n-ary semigroup structures defined by polynomial functions over infinite commutative integral domains with identity, thus generalizing G{\l}azek and Gleichgewicht's classification of the corresponding ternary semigroups.