论文标题
几乎戈伦斯坦（Gorenstein）与戈伦斯坦（Gorenstein
Nearly Gorenstein vs almost Gorenstein affine monomial curves
论文作者
论文摘要
我们将几乎Gorenstein仿射单曲线的一些结果扩展到了几乎Gorenstein的情况。特别是，我们证明了$ \ mathbb {a}^4 $最多$ 3 $的Cohen-Macaulay类型几乎是Gorenstein单一曲线，在这种情况下，回答了Stamate的问题。此外，我们证明，如果$ \ Mathcal c $是几乎是Gorenstein仿射单曲线，不是Gorenstein，而$ n_1，\ dots，n_ν$是相关数值半群的最低生成器每$ $ $ $ $。
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 which is not Gorenstein and $n_1, \dots, n_ν$ are the minimal generators of the associated numerical semigroup, the elements of $\{n_1, \dots, \widehat{n_i}, \dots, n_ν\}$ are relatively coprime for every $i$.
