A Generalized Davenport Constant of the Second Kind

2025/06/16 by Jared Kettinger, Kettinger, Jared
Mathematics · #11R65 (Secondary) #13A05 (Primary) 11R04 #Advanced Optimization Algorithms Research #Commutative Algebra (math.AC) #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2506.13532

openalex publication_date 2025/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Elasticity of Orders with Prime Conductor
• On monoids of weighted zero-sum sequences and applications to norm monoids in Galois number fields and binary quadratic forms
• The interplay of Invariant Theory with Multiplicative Ideal Theory and with Arithmetic Combinatorics
• The Large Davenport Constant II: General Upper Bounds
• The Large Davenport Constant I: Groups with a Cyclic, Index 2 Subgroup

Related

• Davenport constant for commutative rings
• A classification of finite groups with small Davenport constant
• The interplay of Invariant Theory with Multiplicative Ideal Theory and with Arithmetic Combinatorics
• Combinatorial invariants for certain classes of non-abelian groups
• Davenport constant and its variants for some non-abelian groups