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

Abstract

Let $G$ be an additive abelian group. A sequence $S=g_1\cdot \dots \cdot g_{\ell }$ of terms from $G$ is a plus-minus weighted zero-sum sequence if there are ${𝜀}_1,\dots ,{𝜀}_{\ell }\in \{1,-1\}$ such that ${𝜀}_1{g}_1+\dots +{𝜀}_{\ell }{g}_{\ell }=0$. We first characterize (in terms of $G$) when the monoid ${\mathcal{ℬ}}_{\pm }(G)$ 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.