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Asymptotic behavior of reduction numbers

Author: Lê Tuân Hoa
Journal: Proc. Amer. Math. Soc. 130 (2002), 3151-3158
MSC (1991): Primary 13A15
Published electronically: April 17, 2002
MathSciNet review: 1912991
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Abstract: It is shown that the reduction number and the big reduction number of $S/I^n$ are linear functions of $n$ for all large $n$. Here $I$ is a homogeneous ideal of a polynomial ring $S$.

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  • [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

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

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