Abstract

Good semigroups form a class of submonoids of ${\mathbb{N}}^d$ containing the value semigroups of curve singularities. In this article, we describe a partition of the complement of good semigroup ideals. As main application, we describe the Apéry sets of good semigroups with respect to arbitrary elements. This generalizes to any $d\ge 2$ the results in the study of D’Anna et al., which are proved in the case d = 2 and only for the standard Apéry set with respect to the smallest nonzero element. Several new results describing good semigroups in ${\mathbb{N}}^d$ are also provided.

中文翻译：

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好的半群理想和 Apéry 集的补集的划分

摘要

好的半群形成一类子幺半群 ${\mathbb{N}}^d$包含曲线奇异点的值半群。在本文中，我们描述了良好半群理想的补集的划分。作为主要应用，我们描述了关于任意元素的好半群的 Apéry 集。这推广到任何$d\ge 2$D'Anna 等人的研究结果在d  = 2的情况下得到证明，并且仅适用于关于最小非零元素的标准 Apéry 集。描述良好半群的几个新结果${\mathbb{N}}^d$ 还提供。