Asymptotic behavior of reduction numbers

Author:
Lê Tuân Hoa

Journal:
Proc. Amer. Math. Soc. **130** (2002), 3151-3158

MSC (1991):
Primary 13A15

DOI:
https://doi.org/10.1090/S0002-9939-02-06440-7

Published electronically:
April 17, 2002

MathSciNet review:
1912991

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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that the reduction number and the big reduction number of are linear functions of for all large . Here is a homogeneous ideal of a polynomial ring .

**[BH]**H. Bresinsky and L. T. Hoa,*On the reduction number of some graded algebras*, Proc. Amer. Math. Soc.**127**(1999), 1257-1263. MR**99h:13027****[CHT]**D. Cutkosky, J. Herzog and N. V. Trung,*Asymptotic behaviour of the Castelnuovo-Mumford regularity*, Compositio math.**118**(1999), 243-261. MR**2000f:13037****[HHT]**J. Herzog, L. T. Hoa and N. V. Trung,*Asymptotic linear bounds for the Castelnuovo-Mumford regularity*, Trans. Amer. Math. Soc. (to appear).**[H]**L. T. Hoa,*Reduction numbers and Rees algebras of powers of an ideal*, Proc. Amer. Math. Soc.**119**(1993), 415-422. MR**93k:13009****[K]**V. Kodiyalam,*Asymptotic behaviour of Castelnuovo-Mumford regularity*, Proc. Amer. Math. Soc.**128**(2000), 407-411. MR**2000c:13027****[NR]**D. G. Northcott and D. Rees,*Reductions of ideals in local rings*, Proc. Cambridge Philos. Soc.**50**(1954), 145-158. MR**15:596a****[S]**J. Sally,*Reductions, local cohomology and Hilbert functions of local rings*, Commutative Algebra (Durham 1981), London Math. Soc. Lecture Note Ser., vol. 72, Cambridge Univ. Press, Cambridge and New York, 1982, pp. 231-241. MR**84g:13037****[T1]**N. V. Trung,*Reduction exponent and degree bound for the defining equations of graded rings*, Proc. Amer. Math. Soc.**101**(1987), 229-236. MR**89i:13031****[T2]**N. V. Trung,*Gröbner bases, local cohomology and reduction number*, Proc. Amer. Math. Soc.**129**(2001), 9-18. MR**2001c:13042****[V1]**W. V. Vasconcelos, Computational Methods in Commutative Algebra and Algebraic Geometry, Springer-Verlag, Berlin, 1998. MR**99c:13048****[V2]**W. V. Vasconcelos,*Reduction numbers of ideals*, J. Algebra**216**(1999), 652-664. MR**2000e:13005**

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Additional Information

**Lê Tuân Hoa**

Affiliation:
Institute of Mathematics, Box 631, Bò Hô, 10000 Hanoi, Vietnam

Email:
lthoa@thevinh.ncst.ac.vn

DOI:
https://doi.org/10.1090/S0002-9939-02-06440-7

Keywords:
Reduction number,
Castelnuovo-Mumford regularity

Received by editor(s):
March 23, 2001

Received by editor(s) in revised form:
June 5, 2001

Published electronically:
April 17, 2002

Additional Notes:
The author was supported by the National Basic Research Program (Vietnam) and University of Essen (Germany)

Communicated by:
Wolmer V. Vasconcelos

Article copyright:
© Copyright 2002
American Mathematical Society