Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-10T14:12:00.943Z Has data issue: false hasContentIssue false
  • English
  • Français

On the core of ideals

Published online by Cambridge University Press:  01 December 2004

Craig Huneke  and
Ngô Viêt Trung
Craig Huneke
Affiliation:
Department of Mathematics, University of Kansas, Lawrence, KS 66045-7523, USAhuneke@math.ukans.edu
Ngô Viêt Trung
Affiliation:
Institute of Mathematics, Box 631, Bò Hô, 10000 Hanoi, Vietnamnvtrung@math.ac.vn
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper studies the core of an ideal in a Noetherian local or graded ring. By definition, the core of an ideal is the intersection of all reductions of the ideal. We provide computational formulae for the determination of the core of a graded ring, meaning the core of the unique homogeneous maximal ideal. We then apply the formulae to give answers to several questions raised by Corso, Polini and Ulrich. We are also able to answer in the positive a conjecture raised by these three authors concerning a closed formula for the core. We give a positive answer to their question in the case in which the ring is Cohen–Macaulay with a residue field of characteristic 0, and in the case the ideal is equimultiple.

Keywords

minimal reductioncoregeneric element13A02
Type
Research Article
Information
Compositio Mathematica , Volume 141 , Issue 1 , January 2005 , pp. 1 - 18
Copyright
Foundation Compositio Mathematica 2005