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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
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?)

  • 1. C. Huneke, Complete ideals in two-dimensional regular local rings, Microprogram in Commutative Algebra, MSRI, Springer-Verlag (1987).
  • 2. C. Huneke and J. Sally, Birational extensions in dimension two and integrally closed ideal s, J. of Algebra 115 (2) (1988), 481-500. MR 89e:13025
  • 3. J. Lipman, Rational singularities, with applications to algebraic surfaces and unique factorization, Inst. Hautes Études Sci. Publ. Math. 36 (1969), 195-279. MR 43:1986
  • 4. H. Matsumura, Commutative ring theory, Cambridge Studies in Advanced Math. 8, Cambridge Univ. Press, Cambridge, 1986. MR 88h:13001
  • 5. M. Nagata, Local Rings, Interscience, New York, 1962. MR 27:5790
  • 6. D. G. Northcott and D. Rees, Reductions of ideals in local rings, Proc. Cambridge Phil. Soc. 50 (1954), 145-158. MR 15:596a
  • 7. O. Zariski and P. Samuel, Commutative Algebra Vol.II, Von Nostrand, Princeton, 1960. MR 22:11006

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Additional Information

Mee-Kyoung Kim
Affiliation: Department of Mathematics, Sung Kyun Kwan University, Suwon 440-746, Korea

Received by editor(s): April 28, 1993
Communicated by: Eric M. Friedlander
Article copyright: © Copyright 1997 American Mathematical Society

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