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
Full-text PDF Free Access
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] Henrik Bresinsky and Lê Tuân Hoa, On the reduction number of some graded algebras, Proc. Amer. Math. Soc. 127 (1999), no. 5, 1257–1263. MR 1473657, https://doi.org/10.1090/S0002-9939-99-04622-5
- [CHT] S. Dale Cutkosky, Jürgen Herzog, and Ngô Viêt Trung, Asymptotic behaviour of the Castelnuovo-Mumford regularity, Compositio Math. 118 (1999), no. 3, 243–261. MR 1711319, https://doi.org/10.1023/A:1001559912258
- [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] Lê Tu\cfac{a}n Hoa, Reduction numbers and Rees algebras of powers of an ideal, Proc. Amer. Math. Soc. 119 (1993), no. 2, 415–422. MR 1152984, https://doi.org/10.1090/S0002-9939-1993-1152984-0
- [K] Vijay Kodiyalam, Asymptotic behaviour of Castelnuovo-Mumford regularity, Proc. Amer. Math. Soc. 128 (2000), no. 2, 407–411. MR 1621961, https://doi.org/10.1090/S0002-9939-99-05020-0
- [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] Judith D. Sally, Reductions, local cohomology and Hilbert functions of local rings, Commutative algebra: Durham 1981 (Durham, 1981) London Math. Soc. Lecture Note Ser., vol. 72, Cambridge Univ. Press, Cambridge-New York, 1982, pp. 231–241. MR 693638
- [T1] Ngô Vi\cfudot{e}t Trung, Reduction exponent and degree bound for the defining equations of graded rings, Proc. Amer. Math. Soc. 101 (1987), no. 2, 229–236. MR 902533, https://doi.org/10.1090/S0002-9939-1987-0902533-1
- [T2] Ngô Viêt Trung, Gröbner bases, local cohomology and reduction number, Proc. Amer. Math. Soc. 129 (2001), no. 1, 9–18. MR 1695103, https://doi.org/10.1090/S0002-9939-00-05503-9
- [V1] Wolmer V. Vasconcelos, Computational methods in commutative algebra and algebraic geometry, Algorithms and Computation in Mathematics, vol. 2, Springer-Verlag, Berlin, 1998. With chapters by David Eisenbud, Daniel R. Grayson, Jürgen Herzog and Michael Stillman. MR 1484973
- [V2] Wolmer V. Vasconcelos, Reduction numbers of ideals, J. Algebra 216 (1999), no. 2, 652–664. MR 1692969, https://doi.org/10.1006/jabr.1998.7803
Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 13A15
Retrieve articles in all journals with MSC (1991): 13A15
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
