The numerical duplication of a numerical semigroup

الأصل · EN

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 Sᵇ (where b is any odd integer belonging to S), such that S=(Sᵇ)/2. In particular, we characterize the ideals E such that SᵇE is almost symmetric and we determine its type.