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 {mathbb {A}}^4 is at most 3, answering a question of Stamate in this particular case. Moreover, we prove that, if {mathcal {C}} is a nearly Gorenstein affine monomial curve that is not Gorenstein and n_1, dots , n_{nu } are the minimal generators of the associated numerical semigroup, the elements of {n_1, dots , widehat{n_i}, dots , n_{nu }} are relatively coprime for every i.
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