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RELATIVE HILBERT CO-EFFICIENTS

Published online by Cambridge University Press:  01 March 2017

AMIR MAFI
Affiliation:
Department of Mathematics, University of Kurdistan, P.O. Box: 416, Sanandaj, Iran e-mail: [email protected]
TONY J. PUTHENPURAKAL
Affiliation:
Department of Mathematics, IIT Bombay, Powai, Mumbai 400 076, India e-mails: [email protected], [email protected]
RAKESH B. T. REDDY
Affiliation:
Department of Mathematics, IIT Bombay, Powai, Mumbai 400 076, India e-mails: [email protected], [email protected]
HERO SAREMI
Affiliation:
Department of Mathematics, Sanandaj Branch, Islamic Azad University, Sanandaj, Iran e-mail: [email protected]
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Abstract

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Let (A, ${\mathfrak{m}$) be a Cohen–Macaulay local ring of dimension d and let IJ be two ${\mathfrak{m}$-primary ideals with I a reduction of J. For i = 0,. . .,d, let eiJ(A) (eiI(A)) be the ith Hilbert coefficient of J (I), respectively. We call the number ci(I, J) = eiJ(A) − eiI(A) the ith relative Hilbert coefficient of J with respect to I. If GI(A) is Cohen–Macaulay, then ci(I, J) satisfy various constraints. We also show that vanishing of some ci(I, J) has strong implications on depth GJn(A) for n ≫ 0.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2017 

References

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