Equimultiple coefficient ideals

• P. H. Lima ^[1] ; V. H. Jorge Pérez ^[1]
  1. [1] Universidade de São Paulo

     Universidade de São Paulo

     Brasil

     
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 121, Nº 1, 2017, págs. 5-18
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let (R,m) be a quasi-unmixed local ring and I an equimultiple ideal of R of analytic spread s. In this paper, we introduce the equimultiple coefficient ideals. Fix k∈{1,…,s}. The largest ideal L containing I such that ei(Ip)=ei(Lp) for each i∈{1,…,k} and each minimal prime p of I is called the k-th equimultiple coefficient ideal denoted by Ik. It is a generalization of the coefficient ideals introduced by Shah for the case of m-primary ideals. We also see applications of these ideals. For instance, we show that the associated graded ring GI(R) satisfies the S1 condition if and only if In=(In)1 for all n.