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An Inequality Involving Tight Closure and Parameter Ideals |
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| Authors: | Ciuperca Catalin; Enescu Florian |
| Institution: | Department of Mathematics, University of Missouri Columbia, MO 65211, USA ciuperca{at}math.ucr.edu Department of Mathematics, University of Utah Salt Lake City, UT 84112, USA enescu{at}math.utah.edu The Institute of Mathematics of the Romanian Academy Bucharest, Romania |
| Abstract: | An inequality is established involving colengths of the tightclosure of ideals of systems of parameters in local rings withsome mild conditions. As an application, a proof is given ofa result due to Goto and Nakamura (first conjectured by Watanabeand Yoshida), which states that the Hilbert–Samuel multiplicityof a parameter ideal is greater than or equal to the colengthof the tight closure of the ideal. The result is also furtherrefined. 2000 Mathematics Subject Classification 13D40, 13A35,13H15. |
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