### Abstract

Let Q be a parameter ideal in a Noetherian local ring A with the maximal ideal m. Then A is a regular local ring and m/Q is cyclic, if depth A > 0 and Q^{n} is m-full for some integer n ≥ 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 ≥ 1.

Original language | English |
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Pages (from-to) | 405-411 |

Number of pages | 7 |

Journal | Tokyo Journal of Mathematics |

Volume | 29 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Jan 2006 |

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## Cite this

Matsuoka, N. (2006). On m-full powers of parameter ideals.

*Tokyo Journal of Mathematics*,*29*(2), 405-411. https://doi.org/10.3836/tjm/1170348175