Partition of the complement of good semigroup ideals and Apéry sets. Issue 10 (4th August 2021)

• Record Type: Journal Article
• Authors: Guerrieri, L.; Maugeri, N.; Micale, V.
• Is Part Of: Communications in algebra. Volume 49:Issue 10(2021)
• Page Start: 4136
• Page End: 4158
• Publication Date: 2021-08-04
• Subjects: Apéry set -- good semigroups; 20M10 -- 20M14 -- 20M25; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2021.1915325
• Languages: English
• ISSNs: 0092-7872

Abstract

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 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 ≥ 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 N d are also provided.