讲座内容：

Let S ⊆ N 0 be a numerical monoidand let P fin (S), resp P fin,0 (S), denote the power monoid, resp. the restricted power monoid, of S, that is the set of all finite nonempty subsetsof S, resp. the set of all finite nonempty subsets of S containing 0, with setaddition as operation. The arithmetic of power monoids received some attentionin recent literature, in particular in works of Tringali. We complement these investigations by studying algebraic properties of power monoids, such as theirprime spectrum. Moreover, we show that almost all elements of P fin,0 (S) areirreducible (i.e., they are not proper sumsets). This is joint work with AlfredGeroldinger.