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讲座内容：

Let $G$ be an additive abelian group and let $\Gamma \subseteq \mathbb Z$ be a subset. A sequence $S = (g_1, \ldots, g_{\ell}$ of terms from $G$ is a $\Gamma$-weighted zero-sum sequence if there are $\gamma_1, \ldots, \gamma_{\ell} \in \Gamma$ such that $\gamma_1 g_1 + \ldots + \gamma_{\ell} g_{\ell} = 0$. Apart from the fundamental case when $\Gamma = \{1\}$, one of the most studied cases is when $\Gamma = \{\pm 1\}$.

Weighted zero-sum problems have been investigated in the literature for roughly twenty years. Fresh impetus has come from connections to algebraic problems arising in Ring Theory and Factorization Theory. We will highlight these connections and consider algebraic and arithmetic properties of the monoid $\mathcal B_{\Gamma}(G)$ of all $\Gamma$-weighted zero-sum sequences over $G$.