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

 

On Burch's inequality and a reduction system of a filtration


Authors: Y. Kinoshita, K. Nishida, Y. Yamanaka and A. Yoneda
Journal: Proc. Amer. Math. Soc. 134 (2006), 3437-3444
MSC (2000): Primary 13A02, 13A30
Published electronically: June 9, 2006
MathSciNet review: 2240653
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Abstract: Let $ \mathcal{F} = \{ F_n \}$ be a multiplicative filtration of a local ring such that the Rees algebra $ \mathrm{R}(\mathcal{F})$ is Noetherian. We recall Burch's inequality for $ \mathcal{F}$ and give an upper bound of the a-invariant of the associated graded ring $ \mathrm{a}(\mathrm{G}(\mathcal{F}))$ using a reduction system of $ \mathcal{F}$. Applying those results, we study the symbolic Rees algebra of certain ideals of dimension $ 2$.


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Additional Information

Y. Kinoshita
Affiliation: Division of Mathematical Sciences and Physics, School of Science and Technology, Chiba University, 263-8522, Japan

K. Nishida
Affiliation: Division of Mathematical Sciences and Physics, School of Science and Technology, Chiba University, 263-8522, Japan
Email: nishida@math.s.chiba-u.ac.jp

Y. Yamanaka
Affiliation: Division of Mathematical Sciences and Physics, School of Science and Technology, Chiba University, 263-8522, Japan

A. Yoneda
Affiliation: Division of Mathematical Sciences and Physics, School of Science and Technology, Chiba University, 263-8522, Japan

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08429-2
PII: S 0002-9939(06)08429-2
Keywords: Multiplicative filtration, Rees algebra, associated graded ring
Received by editor(s): April 22, 2004
Received by editor(s) in revised form: July 1, 2005
Published electronically: June 9, 2006
Additional Notes: The second author was supported by the Grant-in-Aid for Scientific Researches in Japan (C) (2) No. 15540009
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2006 American Mathematical Society