An inequality involving tight closure and parameter ideals

Details An inequality involving tight closure and parameter ideals An inequality involving tight closure and parameter ideals

2003-06-24

arxiv.org/abs/math/0306349v1

Mathematics

Commutative Algebra

8 pages, to appear in Bull. London Math. Soc

Scientific paper

We establish an inequality involving colengths of the tight closure of ideals of systems of parameters in local rings with some mild conditions. As an application, we prove and refine a result by Goto and Nakamura, conjectured by Watanabe and Yoshida, which states that the Hilbert-Samuel multiplicity of a parameter ideal is greater than or equal to the colength of the tight closure of the ideal.

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