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 \(S\bowtie ^b E\). 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 \(S\bowtie ^b E\) work. In particular, we characterize the ideals E such that \(S\bowtie ^b E\) is nearly Gorenstein.

中文翻译：

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理想的复制品

在本文中，我们提出并研究了理想重复，这是数值半群S的相对理想类中的一种新构造，它在特定假设下产生数值重复的相对理想\(S\bowtie ^b E\ )。我们证明了数值重复的每一个相对理想都可以唯一地写成S的两个相对理想的理想重复；这使我们能够更好地理解\(S\bowtie ^b E\)的相对理想的类的基本操作是如何工作的。特别地，我们刻画了理想E，使得\(S\bowtie ^b E\)接近 Gorenstein。