Pseudo-Frobenius numbers and defining ideals in stretched numerical semigroup rings

2025/01/11 by Van Kien, Van Kien, Do, Naoyuki Matsuoka +3 · 1 citation
Mathematics · #13A02 #13A30 #13D02 #13G05 #20M25 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2501.06415

openalex publication_date 2025/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The pseudo-Frobenius numbers of a numerical semigroup H are deeply connected to the structure of the defining ideal of its semigroup ring k[H]. In this paper, we resolve a certain conjecture related to this connection under the assumption that k[H]/(t^a) is stretched, where a is the multiplicity of H. Furthermore, we provide numerical conditions for the tangent cone of k[H] to be Cohen-Macaulay.

Cited by

• Defining ideals of some numerical semigroup rings with arithmetic pseudo-Frobenius numbers

Related

• Pseudo-Frobenius numbers versus defining ideals in numerical semigroup rings
• Defining ideals of some numerical semigroup rings with arithmetic pseudo-Frobenius numbers
• Tangent Cone of Numerical Semigroup Rings of Embedding Dimension Three
• Tangent cones of numerical semigroup rings
• Tangent cones of monomial curves obtained by numerical duplication