On ideals of affine semigroups and affine semigroups with maximal embedding dimension

2024/05/23 by J. I. García-García, García-García, J. I., R. Tapia-Ramos +3 · 1 citation
Mathematics · #20M12 #20M14 #Advanced Banach Space Theory #Commutative Algebra (math.AC) #FOS: Mathematics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2405.14648

openalex publication_date 2024/05/23 · openalex created_date 2024/05/25 · openalex updated_date 2026/07/28

Abstract

Let S⊆ \mathbb N^p be a semigroup, any P⊆ S is an ideal of S if P+S⊆ P, and an I(S)-semigroup is the affine semigroup P∪ \0\, with P an ideal of S. We characterise the I(S)-semigroups and the ones that also are \mathcal C-semigroups. Moreover, some algorithms are provided to compute all the I(S)-semigroups satisfying some properties. From a family of ideals of S, we introduce the affine semigroups with maximal embedding dimension, characterising them and describing some families.

Cited by

• Buchsbaumness of finite complement simplicial affine semigroups

Related

• Characterizing affine C-semigroups
• Problems and algorithms for affine semigroups
• On some properties for cofiniteness of submonoids and ideals of an affine semigroup
• On unboundedness of some invariants of C-semigroups
• Affine semigroups of maximal projective dimension-II