The numerical duplication of a numerical semigroup

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?S, produces a new numerical semigroup, denoted by S? ^b E (where b is any odd integer belonging to S), such that S=(S? ^b E)/2. In particular, we characterize the ideals E such that S? ^b E is almost symmetric and we determine its type.