Persistence and stability properties of powers of ideals

• Jürgen Herzog ^[1] ; Ayesha Asloob Qureshi ^[2]
  1. [1] University of Duisburg-Essen

     University of Duisburg-Essen

     Kreisfreie Stadt Essen, Alemania

     
  2. [2] The Abdus Salam International Center of Theoretical Physics (Italy)
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 3 ((March 2015)), 2015 (Ejemplar dedicado a: Special Issue in honor of Prof. Hans-Bjørn Foxby), págs. 530-542
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2014.05.011
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• Resumen

  • 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 polymatroidal ideals are bounded by their analytic spread.