Abstract
The aim of this chapter is to study which properties a monoid must fulfill in order to be isomorphic to a numerical semigroup. Levin shows in [46] that if S is finitely generated, Archimedean and without idempotents, then S is multiple joined. By using this as starting point, we will show that a monoid is isomorphic to a numerical semigroup if and only if it is finitely generated, quasi-Archimedean, torsion free and with only one idempotent. We will also relate this characterization with other interesting properties in semigroup theory such as weak cancellativity, being free of units, and being hereditarily finitely generated.
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