The ideal duplication

In this paper we present and study the ideal duplication, a new construction within the class of the relative ideals of a numerical semigroup S, that, under specific assumptions, produces a relative ideal of the numerical duplication S sic(b)E. We prove that every relative ideal of the numerical duplication can be uniquely written as the ideal duplication of two relative ideals of S; this allows us to better understand how the basic operations of the class of the relative ideals of Ssic(b)E work. In particular, we characterize the ideals E such that Ssic(b)E is nearly Gorenstein.