The multiples of a numerical semigroup.

Given two numerical semigroups S and T we say that T is a multiple of S if there exists an integer d ∈ N \ {0} such that S = {x ∈ N | dx ∈ T}. In this paper we study the family of multiples of a (fixed) numerical semigroup. We also address the open problem of finding numerical semigroups of embedding dimension e without any quotient of embedding dimension less than e, and provide new families with this property. [ABSTRACT FROM AUTHOR]