Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids. (English) Zbl 1474.20117

Summary: Arithmetical invariants – such as sets of lengths, catenary and tame degrees – describe the non-uniqueness of factorizations in atomic monoids. We study these arithmetical invariants by the monoid of relations and by presentations of the involved monoids. The abstract results will be applied to numerical monoids and to Krull monoids.


20M14 Commutative semigroups
20M13 Arithmetic theory of semigroups
13A05 Divisibility and factorizations in commutative rings


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