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Rosales, J. C.

On numerical semigroups. (English) Zbl 0853.20041

Semigroup Forum 52, No. 3, 307-318 (1996).
A numerical semigroup \(S\) is an additive submonoid of \(\mathbb{N}\) such that \(\mathbb{N}-S\) is finite. For a numerical semigroup \(S\), its conductor \(C\) is the largest integer not in \(S\), its multiplicity is the smallest positive integer \(m\) in \(S\), and the embedding dimension of \(S\) is the number of minimal generators of \(S\). In this paper, the author investigates the relationship between the two numerical semigroups \(S\) and \(S'=S\cup\{C\}\), and uses this to study the set \(S(m)\) of all numerical semigroups with multiplicity \(m\). The author also studies those numerical semigroups \(S\) with multiplicity equal to embedding dimension, i.e., with maximal embedding dimension in \(S(m)\).
Reviewer: D.F.Anderson (Knoxville)

Cited in 1 Review
Cited in 12 Documents

MSC:

20M14 Commutative semigroups

Keywords:

conductor; multiplicity; embedding dimension; number of minimal generators; numerical semigroups
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\textit{J. C. Rosales}, Semigroup Forum 52, No. 3, 307--318 (1996; Zbl 0853.20041)
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