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⋈bE. 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⋈bE work. In particular, we characterize the ideals E such that S⋈bE is nearly Gorenstein.
Troia, D. (2021). The ideal duplication. SEMIGROUP FORUM, 103(2), 641-660 [10.1007/s00233-021-10201-1].
The ideal duplication
Troia, Danny
2021-01-01
Abstract
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⋈bE. 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⋈bE work. In particular, we characterize the ideals E such that S⋈bE is nearly Gorenstein.
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