On Monoids of plus-minus weighted Zero-Sum Sequences: The Isomorphism Problem and the Characterization Problem

2023/04/28 by Fabsits, Florin, Geroldinger, Alfred, Reinhart, Andreas +1 · 1 citation
#11B30 #11R27 #13A05 #13A15 #20M12 #20M13 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.14777

Abstract

Let G be an additive abelian group. A sequence S=g₁⋅…⋅ g_ℓ of terms from G is a plus-minus weighted zero-sum sequence if there are ε₁,…,ε_ℓ∈\-1,1\ such that ε₁ g₁+…+ε_ℓ g_ℓ=0. We first characterize (in terms of G) when the monoid B_±(G) of plus-minus weighted zero-sum sequences is Mori resp. Krull resp. finitely generated. After that we study the Isomorphism and the Characterization Problem for monoids of plus-minus weighted zero-sum sequences.

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