Additive decomposability of functions over abelian groups

TL;DR

This paper explores how functions over abelian groups can be decomposed additively, revealing a classification based on specific additive decompositions related to the arity gap of 2.

Contribution

It introduces a new classification of abelian group functions based on additive decomposability tied to the arity gap of 2.

Findings

Functions are classified by additive decompositions.

Decompositions relate to the arity gap of 2.

Provides a framework for understanding function structure over abelian groups.

Abstract

Abelian groups are classified by the existence of certain additive decompositions of group-valued functions of several variables with arity gap 2.