Irreducible numerical semigroups having Toms decomposition
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SourceCommunications in Algebra 35(1) (2007), 1-13
In this article we prove that if S is an irreducible numerical semigroup and S is generated by an interval or S has multiplicity 3 or 4, then it enjoys Toms decomposition. We also prove that if a numerical semigroup can be expressed as an expansion of a numerical semigroup generated by an interval, then it is irreducible and has Toms decomposition.