The stable set of associated prime ideals of a squarefree principal Borel ideal

TL;DR

This paper investigates the properties of squarefree principal Borel ideals, demonstrating their persistence property for associated primes and explicitly determining their stable associated prime ideals and stability index.

Contribution

It establishes the persistence property for these ideals and computes their stability index and stable associated primes, providing new insights into their algebraic structure.

Findings

Squarefree principal Borel ideals satisfy the persistence property.

The index of stability for these ideals is explicitly computed.

The stable set of associated prime ideals is determined.

Abstract

It is shown that a squarefree principal Borel ideal satisfies the persistence property for the associated prime ideals. For the graded maximal ideal we compute the index of stability with respect to squarefree principal Borel ideals and determine their stable set of associated prime ideals.