Factorization of an integrally closed ideal

in two-dimensional regular local rings

Author:
Mee-Kyoung Kim

Journal:
Proc. Amer. Math. Soc. **125** (1997), 3509-3513

MSC (1991):
Primary 13A18; Secondary 13B20, 13C05

MathSciNet review:
1415330

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Abstract: Let be a two-dimensional regular local ring with algebraically closed residue field and be an -primary integrally closed ideal in . Let be the set of Rees valuations of and be the residue field of the valuation ring associated with . Assume that is any minimal reduction of . We show that if is the product of the distinct simple -primary integrally closed ideals in , then is generated by the image of over for all , and the converse of this is also true.

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Additional Information

**Mee-Kyoung Kim**

Email:
mkkim@yurim.skku.ac.kr

DOI:
https://doi.org/10.1090/S0002-9939-97-04064-1

Received by editor(s):
July 16, 1993

Received by editor(s) in revised form:
July 12, 1996

Communicated by:
Wolmer V. Vasconcelos

Article copyright:
© Copyright 1997
American Mathematical Society