A Generalized Davenport Constant of the Second Kind

TL;DR

This paper investigates a ring invariant related to the Davenport constant, calculating it for specific rings of integers and Galois-invariant orders to shed light on their factorization properties.

Contribution

It introduces a generalized Davenport constant of the second kind and computes it for certain rings, linking it to factorization characteristics.

Findings

Calculated the invariant for rings of integers and their orders.

Connected the invariant to factorization properties.

Analyzed Galois-invariant orders for well-behaved cases.

Abstract

In this paper, we explore a ring invariant which is closely related to the Davenport constant of a group. In particular, we will calculate this invariant for a certain class of rings of integers and their orders and use it to understand factorization properties of the latter. To this end, we also examine the well-behaved class of Galois-invariant orders.