Persistence and stability properties of powers of ideals

  title={Persistence and stability properties of powers of ideals},
  author={J. Herzog and A. Qureshi},
  journal={Journal of Pure and Applied Algebra},
  • J. Herzog, A. Qureshi
  • Published 2012
  • Mathematics
  • Journal of Pure and Applied Algebra
  • 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
    49 Citations

    Figures from this paper.


    On linear resolution of powers of an ideal
    • 10
    • PDF
    Associated primes of powers of edge ideals
    • 60
    • Highly Influential
    • PDF
    Monomial localizations and polymatroidal ideals
    • 12
    • PDF
    The Stable Set of Associated Primes of the Ideal of a Graph
    • 53
    Replication in critical graphs and the persistence of monomial ideals
    • 28
    • PDF
    A conjecture on critical graphs and connections to the persistence of associated primes
    • 24
    • PDF
    Cohen-Macaulay Rings
    • 2,360