On monoids of weighted zero-sum sequences and applications to norm monoids in Galois number fields and binary quadratic forms

2022/02/24 by Alfred Geroldinger, Geroldinger, Alfred, Franz Halter‐Koch +3 · 3 citations
Computer Science · Mathematics · #11B50 #11B75 #11E12 #11R27 #20M13 #Advanced Topology and Set Theory #Coding theory and cryptography #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Computability, Logic, AI Algorithms #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2202.12054

openalex publication_date 2022/02/24 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

Let G be an additive finite abelian group and Γ⊂ End (G) be a subset of the endomorphism group of G. A sequence S = g₁ ⋅ … ⋅ g_ℓ over G is a (Γ-)weighted zero-sum sequence if there are γ₁, …, γ_ℓ ∈ Γ such that γ₁ (g₁) + … + γ_ℓ (g_ℓ)=0. We construct transfer homomorphisms from norm monoids (of Galois algebraic number fields with Galois group Γ) and from monoids of positive integers, represented by binary quadratic forms, to monoids of weighted zero-sum sequences. Then we study algebraic and arithmetic properties of monoids of weighted zero-sum sequences.

Cited by

• Galois Action and Localization in Number Fields
• The set of minimal distances of the monoid of plus-minus weighted zero-sum sequences and applications to the characterization problem
• A Generalized Davenport Constant of the Second Kind

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