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Erschienen in:
18.02.2020 | Original Paper
Numerical semigroups closed under addition of their divisors
Erschienen in: Applicable Algebra in Engineering, Communication and Computing | Ausgabe 6/2021
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Abstract
A numerical semigroup S is closed under addition of its divisors (\({\mathcal {C}}\)-semigroup) if the following condition holds: if \(s\in S\setminus \{0\}\) and d is a non trivial divisor of s then \(s+d\in S\). In this paper we prove that the set of all \({\mathcal {C}}\)-semigroups is a Frobenius variety. As a consequence, we give algorithms to compute the set \({\mathcal {C}}\)-semigroups with fixed multiplicity, genus and Frobenius number.