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A Generalized Davenport Constant of the Second Kind

Jared Kettinger

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.

A Generalized Davenport Constant of the Second Kind

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.

Paper Structure

This paper contains 3 sections, 11 theorems, 16 equations.

Table of Contents

  1. Introduction and notation
  2. Conditions for finite elasticity of orders in rings of integers
  3. Elasticity of orders in quadratic number fields

Key Result

Theorem 1.4

Let $R$ be a ring of integers with class number $h > 1$. Then

Theorems & Definitions (35)

  • Definition 1.1
  • Definition 1.2
  • Definition 1.3
  • Theorem 1.4: Narkiewicz1995Note
  • Example 1.5
  • Definition 1.6
  • Definition 1.7
  • Example 1.8
  • Lemma 2.1
  • proof
  • ...and 25 more