Generators of a fraction of a numerical semigroup

Abstract

Given a numerical semigroup $S$ and a positive integer $d$, the fraction $S/d=\{ x \in \mathbb {N} \mid dx \in S\}$ is again a numerical semigroup. In this paper we determine a generating set for $S/d$ in terms of the minimal generators of $S$ and provide sharp upper bounds for the embedding dimension of $S/d$.