ON MONOIDS OF PLUS-MINUS WEIGHTED ZERO-SUM SEQUENCES: THE ISOMORPHISM PROBLEM AND THE CHARACTERIZATION PROBLEM

Florin Fabsits, Alfred Geroldinger, Andreas Reinhart, Qinghai Zhong

Type: Article

Publication Date: 2024-01-18

Citations: 0

DOI: https://doi.org/10.1216/jca.2024.16.1

Abstract

Let G be an additive abelian group. A sequence S=g1⋅…⋅gℓ of terms from G is a plus-minus weighted zero-sum sequence if there are 𝜀1,…,𝜀ℓ∈{1,−1} such that 𝜀1g1+…+𝜀ℓgℓ=0. We first characterize (in terms of G) when the monoid ℬ±(G) of plus-minus weighted zero-sum sequences is Mori, respectively, Krull, respectively, finitely generated. After that, we study the isomorphism problem and the characterization problem for monoids of plus-minus weighted zero-sum sequences.

Locations

Journal of Commutative Algebra - View
arXiv (Cornell University) - View - PDF

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