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An Inequality Involving Tight Closure and Parameter Ideals
Author(s) -
Ciuperca Catalin,
Enescu Florian
Publication year - 2004
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609303002923
Subject(s) - mathematics , closure (psychology) , multiplicity (mathematics) , inequality , ideal (ethics) , pure mathematics , mathematics subject classification , discrete mathematics , calculus (dental) , mathematical analysis , law , political science , medicine , dentistry
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. 2000 Mathematics Subject Classification 13D40, 13A35, 13H15.