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December 2006 On $\frak{m}$-Full Powers of Parameter Ideals
Naoyuki MATSUOKA
Tokyo J. Math. 29(2): 405-411 (December 2006). DOI: 10.3836/tjm/1170348175

Abstract

Let $Q$ be a parameter ideal in a Noetherian local ring $A$ with the maximal ideal $\frak{m}$. Then $A$ is a regular local ring and $\frak{m}/Q$ is cyclic, if $\rm{depth}\ A > 0$ and $Q^n$ is $\frak{m}$-full for some integer $n \geq 1$. Consequently, $A$ is a regular local ring and all the powers of $Q$ are integrally closed in $A$ once $Q^n$ is integrally closed for some $n \geq 1$.

Citation

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Naoyuki MATSUOKA. "On $\frak{m}$-Full Powers of Parameter Ideals." Tokyo J. Math. 29 (2) 405 - 411, December 2006. https://doi.org/10.3836/tjm/1170348175

Information

Published: December 2006
First available in Project Euclid: 1 February 2007

zbMATH: 1121.13023
MathSciNet: MR2284980
Digital Object Identifier: 10.3836/tjm/1170348175

Subjects:
Primary: 13H05
Secondary: 13H15

Rights: Copyright © 2006 Publication Committee for the Tokyo Journal of Mathematics

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Vol.29 • No. 2 • December 2006
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