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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]

It is shown that strong atoms are rather abundant in monadically Krull monoids. An application to rings of integer-valued polynomials on Krull domains yields new results on strong atoms in these rings. [ABSTRACT FROM AUTHOR]

Correction to: Semigroup Forum https://doi.org/10.1007/s00233-021-10231-9 This article was updated to remove two insertions and an error inadvertently introduced after the author had completed proofreading. The original article can be found online at https://doi.org/10.1007/s00233-021-10231-9. Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. [Extracted from the article]