Pseudo-Frobenius numbers versus defining ideals in numerical semigroup rings

TL;DR

This paper explores the relationship between pseudo-Frobenius numbers and the defining ideals of numerical semigroup rings, providing structural insights when these numbers are multiples of a fixed integer.

Contribution

It characterizes the structure of the defining ideal of semigroup rings in cases where pseudo-Frobenius numbers are multiples of a fixed integer.

Findings

Describes the structure of defining ideals under specific pseudo-Frobenius number conditions

Provides algebraic characterizations relevant to numerical semigroup rings

Enhances understanding of the interplay between pseudo-Frobenius numbers and ideal structures

Abstract

The structure of the defining ideal of the semigroup ring $k[H]$ of a numerical semigroup $H$ over a field $k$ is described, when the pseudo-Frobenius numbers of $H$ are multiples of a fixed integer.