The numerical duplication of a numerical semigroup

Abstract

In this paper we present and study the numerical duplication of a numerical semigroup, a construction that, starting with a numerical semigroup $S$ and a semigroup ideal $E\subseteq S$, produces a new numerical semigroup, denoted by S\Join^b\E (where $b$ is any odd integer belonging to $S$), such that S=(S\Join^b\E)/2. In particular, we characterize the ideals $E$ such that $S\Join^bE$ is almost symmetric and we determine its type.Comment: 17 pages. Accepted for publication on: Semigroup Foru