The strong Rees property of powers of the maximal ideal and Takahashi–Dao's question

In this paper, we introduce the notion of the strong Rees property (SRP) for m-primary ideals of a Noetherian local ring and prove that any power of the maximal ideal m has its property if the associated graded ring G of m satisfies depthG≥2. As its application, we characterize two-dimensional excel...

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Bibliographic Details
Published in:Journal of algebra 2021-04, Vol.571, p.297-315
Main Authors: Puthenpurakal, Tony J., Watanabe, Kei-ichi, Yoshida, Ken-ichi
Format: Article
Language:English
Subjects:
[formula omitted]-Ideal
Integrally closed ideal
Loewy length
Powers of the maximal ideal
Ratliff–Rush closure
Strong Rees property
The number of minimal generators
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Summary:In this paper, we introduce the notion of the strong Rees property (SRP) for m-primary ideals of a Noetherian local ring and prove that any power of the maximal ideal m has its property if the associated graded ring G of m satisfies depthG≥2. As its application, we characterize two-dimensional excellent normal local domains so that m is a pg-ideal. Finally we ask what m-primary ideals have SRP and state a conjecture which characterizes the case when mn are the only ideals which have SRP.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2018.07.028