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Product of distinct simple integrally closed ideals in 2-dimensional regular local rings


Author: Mee-Kyoung Kim
Journal: Proc. Amer. Math. Soc. 125 (1997), 315-321
MSC (1991): Primary 13H05
DOI: https://doi.org/10.1090/S0002-9939-97-03886-0
MathSciNet review: 1396984
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Abstract: Let $(R,m)$ be a two-dimensional regular local ring and $I$ an $m$-primary integrally closed ideal in $R$. In this paper, we give equivalent conditions for $I$ to be a product of distinct simple $m$-primary integrally closed ideals (i.e., $I = I_{1}\cdots I_{l}$, where $I_{1},\cdots ,I_{l}$ are distinct simple $m$-primary integrally closed ideals of $R$) in terms of the regularity of $R[It]/p$ for all $p \in \text {Min} (mR[It])$ and in terms of how to choose a minimal generating set for $I$ over its minimal reductions.


References [Enhancements On Off] (What's this?)

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Additional Information

Mee-Kyoung Kim
Affiliation: Department of Mathematics, Sung Kyun Kwan University, Suwon 440-746, Korea
Email: mkkim@yurim.skku.ac.kr

DOI: https://doi.org/10.1090/S0002-9939-97-03886-0
Received by editor(s): April 28, 1993
Communicated by: Eric M. Friedlander
Article copyright: © Copyright 1997 American Mathematical Society

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