Indispensable binomials in semigroup ideals

TL;DR

This paper investigates the conditions under which the minimal binomial generating set of a semigroup ideal is unique, focusing on indispensable binomials and their combinatorial properties.

Contribution

It provides new necessary and sufficient conditions for the uniqueness of minimal binomial generators in semigroup ideals based on indispensable binomials.

Findings

Identifies conditions for the uniqueness of minimal binomial generating sets.

Provides a combinatorial description of indispensable binomials.

Establishes criteria linking indispensable binomials to generator uniqueness.

Abstract

In this paper, we deal with the problem of uniqueness of minimal system of binomial generators of a semigroup ideal. Concretely, we give different necessary and/or sufficient conditions for uniqueness of such minimal system of generators. These conditions come from the study and combinatorial description of the so-called indispensable binomials in the semigroup ideal.