We extend some results on almost Gorenstein affine monomial curves to the nearly Gorenstein case. In particular, we prove that the Cohen–Macaulay type of a nearly Gorenstein monomial curve in A4 is at most 3, answering a question of Stamate in this particular case. Moreover, we prove that, if C is a nearly Gorenstein affine monomial curve that is not Gorenstein and n1, ⋯ , nν are the minimal generators of the associated numerical semigroup, the elements of { n1, ⋯ , ni^ , ⋯ , nν} are relatively coprime for every i.

Nearly Gorenstein vs Almost Gorenstein Affine Monomial Curves

Moscariello A.;
2021-01-01

Abstract

We extend some results on almost Gorenstein affine monomial curves to the nearly Gorenstein case. In particular, we prove that the Cohen–Macaulay type of a nearly Gorenstein monomial curve in A4 is at most 3, answering a question of Stamate in this particular case. Moreover, we prove that, if C is a nearly Gorenstein affine monomial curve that is not Gorenstein and n1, ⋯ , nν are the minimal generators of the associated numerical semigroup, the elements of { n1, ⋯ , ni^ , ⋯ , nν} are relatively coprime for every i.
2021
4-generated numerical semigroup
almost Gorenstein ring
Nearly Gorenstein ring
type of a numerical semigroup
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/586050
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