Davenport constant for commutative rings

TL;DR

This paper provides an exact formula for the Davenport constant of any finite commutative ring based on its unit group, extending the concept from finite abelian groups to rings.

Contribution

It introduces a precise formula for the Davenport constant of finite commutative rings, generalizing previous results from abelian groups.

Findings

Exact formula for the Davenport constant in terms of the unit group

Extension of the Davenport constant concept to finite commutative rings

Bridging the gap between group and ring structures in combinatorial invariants

Abstract

The Davenport constant is one measure for how "large" a finite abelian group is. In particular, the Davenport constant of an abelian group is the smallest $k$ such that any sequence of length $k$ is reducible. This definition extends naturally to commutative semigroups, and has been studied in certain finite commutative rings. In this paper, we give an exact formula for the Davenport constant of a general commutative ring in terms of its unit group.