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Reduction numbers and Hilbert polynomials of ideals in higher dimensional CohenMacaulay local rings

Published online by Cambridge University Press:  24 October 2008

Yinghwa Wu
Yinghwa Wu
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907, U.S.A.
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Throughout, (R, m) will denote a d-dimensional CohenMacaulay (CM for short) local ring having an infinite residue field and I an m-primary ideal in R. Recall that an ideal J I is said to be a reduction of I if Ir+1 = JIr for some r 0, and a reduction J of I is called a minimal reduction of I if J is generated by a system of parameters. The concepts of reduction and minimal reduction were first introduced by Northcott and Rees12. If J is a reduction of I, define the reduction number of I with respect to J, denoted by rj(I), to be min {r 0 Ir+1 = JIr}. The reduction number of I is defined as r(I) = min {rj(I)J is a minimal reduction of I}. The reduction number r(I) is said to be independent if r(I) = rj(I) for every minimal reduction J of I.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 111 , Issue 1 , January 1992 , pp. 47 - 56
Copyright
Copyright © Cambridge Philosophical Society 1992

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