Two-Extension of a Numerical Semigroup with Embedding Dimension Two

Abstract

Let S and S' be two numerical semigroups such that S\subseteq S' and let d be a positive integer. We say that S' is a d-extension of S if dS'={dx : x\in S'}\subset S. In this paper we study the set of numerical semigroups S such that S is a 2-extension of <n_1,n_2>.