Persistence and stability properties of powers of ideals

@article{Herzog2012PersistenceAS,
title={Persistence and stability properties of powers of ideals},
author={J. Herzog and A. Qureshi},
journal={Journal of Pure and Applied Algebra},
year={2012},
volume={219},
pages={530-542}
}

We introduce the concept of strong persistence and show that it implies persistence regarding the associated prime ideals of the powers of an ideal. We also show that strong persistence is equivalent to a condition on power of ideals studied by Ratliff. Furthermore, we give an upper bound for the depth of powers of monomial ideals in terms of their linear relation graph, and apply this to show that the index of depth stability and the index of stability for the associated prime ideals of… CONTINUE READING