Product of distinct simple integrally closed ideals in 2-dimensional regular local rings
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Abstract:
Let $(R,m)$ be a two-dimensional regular and $I$ an $m$-primary integrally closed 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 $p \in \operatorname {Min} (mR[It])$ and in terms of how to choose a minimal generating set for $I$ over its minimal reductions.References
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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
- Received by editor(s): April 28, 1993
- Communicated by: Eric M. Friedlander
- © Copyright 1997 American Mathematical Society
- 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