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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Hilbert coefficients
and the associated graded rings


Author: Hsin-Ju Wang
Journal: Proc. Amer. Math. Soc. 128 (2000), 963-973
MSC (1991): Primary 13A30, 13D40, 13H10
Published electronically: July 28, 1999
MathSciNet review: 1628432
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Abstract: Let $(R, \mathfrak{m})$ be a $d$-dimensional Cohen-Macaulay local ring with infinite residue field. Let $I$ be an $\mathfrak{m}$-primary ideal of $R$. In this paper, we prove that if $\displaystyle \sum _{n=1}^{\infty} \lambda(I^n/I^{n-1}J)-e_1(I)=1$ for some minimal reduction $J$ of $I$, then depth $G(I)\geq d-2$.


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Additional Information

Hsin-Ju Wang
Email: hjwang@math.ccu.edu.tw

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05080-7
PII: S 0002-9939(99)05080-7
Keywords: Hilbert coefficient, associated graded ring
Received by editor(s): October 3, 1997
Received by editor(s) in revised form: May 19, 1998
Published electronically: July 28, 1999
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2000 American Mathematical Society