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Manuscripta Mathematica

, Volume 150, Issue 3–4, pp 499–520 | Cite as

Good ideals and \({p_{g}}\)-ideals in two-dimensional normal singularities

  • Tomohiro OkumaEmail author
  • Kei-ichi Watanabe
  • Ken-ichi Yoshida
Article

Abstract

In this paper, we introduce the notion of \({p_{g}}\)-ideals and \({p_{g}}\)-cycles, which inherits nice properties of integrally closed ideals on rational singularities. As an application, we prove an existence of good ideals for two-dimensional Gorenstein normal local rings. Moreover, we classify all Ulrich ideals for two-dimensional simple elliptic singularities.

Mathematics Subject Classification

Primary 13A35 Secondary 14B05 14J17 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Tomohiro Okuma
    • 1
    Email author
  • Kei-ichi Watanabe
    • 2
  • Ken-ichi Yoshida
    • 2
  1. 1.Department of Mathematical Sciences, Faculty of ScienceYamagata UniversityYamagataJapan
  2. 2.Department of Mathematics, College of Humanities and SciencesNihon UniversityTokyoJapan

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