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

DOI:
https://doi.org/10.1090/S0002-9939-06-08429-2

Published electronically:
June 9, 2006

MathSciNet review:
2240653

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a multiplicative filtration of a local ring such that the Rees algebra is Noetherian. We recall Burch's inequality for and give an upper bound of the a-invariant of the associated graded ring using a reduction system of . Applying those results, we study the symbolic Rees algebra of certain ideals of dimension .

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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:
https://doi.org/10.1090/S0002-9939-06-08429-2

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