On Burch’s inequality and a reduction system of a filtration
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- by Y. Kinoshita, K. Nishida, Y. Yamanaka and A. Yoneda PDF
- Proc. Amer. Math. Soc. 134 (2006), 3437-3444 Request permission
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 $2$.References
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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
- 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
- © Copyright 2006 American Mathematical Society
- 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
- MathSciNet review: 2240653