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AbstractFlatness in categories of modules over rings has been transferred to categories of acts over semigroups by Stenström in 1971. In this note we will focus on commutative cancellative semigroups with unit (“monoids”) and show that this notion is useful too in considering arithmetical questions. The notion of factorable (resp. pre-Schreier) modules is extended to acts over monoids. For example it is shown that these acts can be characterized by flatness. [ABSTRACT FROM AUTHOR]