0000000001233438
AUTHOR
Danny Troia
The ideal duplication
AbstractIn 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 $$S\bowtie ^b E$$ S ⋈ 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 $$S\bowtie ^b E$$ S ⋈ b E work. In particular, we characterize the ideals E such that $$S\bowtie ^b E$$ S ⋈ b E is nearly Gorenstein.
The nearly Gorenstein property for numerical duplications and semitrivial extensions
In this thesis 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 $SJoin^b E$, for some ideal $E$ of $S$. 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 $SJoin^b E$ work. In particular, we characterize the ideals $E$ such that $SJoin^b E$ is nearly Gorenstein. With the aim to generalize this construction to commutative rings with…