Chevalley Warning type results on abelian groups

TL;DR

This paper generalizes the Chevalley Warning Theorems from fields to abelian groups and noncommutative rings by introducing a new notion of degree for functions between abelian groups.

Contribution

It introduces a novel degree concept for functions between abelian groups, extending classical theorems to broader algebraic structures.

Findings

Generalization of Chevalley Warning Theorems to abelian groups

Development of a degree notion for functions between abelian groups

Application to noncommutative rings and prime power order groups

Abstract

We develop a notion of degree for functions between two abelian groups that allows us to generalize the Chevalley Warning Theorems from fields to noncommutative rings or abelian groups of prime power order.