Partition of complement of good ideals and Apéry sets

2020/05/25 by Lorenzo Guerrieri, Guerrieri, Lorenzo, Nicola Maugeri +3
Computer Science · Mathematics · #20M10 #20M14 #20M25 #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2005.12354

openalex publication_date 2020/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Good semigroups form a class of submonoids of ℕ^d containing the value semigroups of curve singularities. In this article, we describe a partition of the complements of good semigroup ideals, having as main application the description of the Apéry sets of good semigroups. This generalizes to any d ≥ 2 the results of a recent paper of D'Anna, Guerrieri and Micale, 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 ℕ^d are also provided.

Related

• Properties and applications of the Apéry set of good semigroups in ℕ^d
• The Apéry Set of a Good Semigroup
• Good subsemigroups of \mathbb Nⁿ
• Almost symmetric good semigroups
• Embedding dimension of a good semigroup