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AN INEQUALITY INVOLVING TIGHT CLOSURE AND PARAMETER IDEALS
Published online by Cambridge University Press: 28 April 2004
Abstract
An inequality is established involving colengths of the tight closure of ideals of systems of parameters in local rings with some mild conditions. As an application, a proof is given of a result due to Goto and Nakamura (first 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. The result is also further refined.
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- © The London Mathematical Society 2004
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