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Let $G$ be an additive abelian group. A sequence $S=g_1\cdot\ldots\cdotg_{\ell}$ of terms from $G$ is a plus-minus weighted zero-sum sequence if thereare $\varepsilon_1,\ldots,\varepsilon_{\ell}\in\{-1,1\}$ such that$\varepsilon_1 g_1+\ldots+\varepsilon_{\ell} g_{\ell}=0$. We first characterize(in terms of $G$) when the monoid $\mathcal{B}_{\pm}(G)$ of plus-minus weightedzero-sum sequences is Mori resp. Krull resp. finitely generated. After that westudy the Isomorphism and the Characterization Problem for monoids ofplus-minus weighted zero-sum sequences.

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