Generators of a fraction of a numerical semigroup. (English) Zbl 1450.20019

Moscariello, Alessio

J. Commut. Algebra 11, No. 3, 389-400 (2019).

In this paper, the authors study the fraction of a numerical semigroup \(S\), that is, the set \(S/d=\{x\in\mathbb{N}\mid dx\in S\}\) with \(d\in\mathbb{N}\). In order to do it, they introduce the notion of \(d\)-partition which is a finite sequence of integers with some properties.
Using this tool, the generating set of the fractions of a numerical semigroup can be determined using its the minimal generating set and a sharp bound for the embedding dimension of these fractions is given. Finally, they give alternative proofs for results which are already in the literature, for example an application to proportionally modular semigroup is showed.
The paper contains all the background needed for being understood and the proofs can be read easily. It is well-written so it is pleasant to read.

Reviewer: Daniel Marín Aragon (Cádiz)

MSC:

20M14

Commutative semigroups

Keywords:

numerical semigroup; embedding dimension

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