An inequality involving tight closure and parameter ideals
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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.
8 pages, to appear in Bull. London Math. Soc
8 pages, to appear in Bull. London Math. Soc