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    Elias, Juan 2013. On the last Hilbert–Samuel coefficient of isolated singularities. Journal of Algebra, Vol. 394, p. 285.


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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 145, Issue 1
  • July 2008, pp. 87-94

Upper bounds of Hilbert coefficients and Hilbert functions

  • JUAN ELIAS (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004108001138
  • Published online: 01 July 2008
Abstract
Abstract

Let (R, m) be a d-dimensional Cohen–Macaulay local ring. In this paper we prove, in a very elementary way, an upper bound of the first normalized Hilbert coefficient of a m-primary ideal IR that improves all known upper bounds unless for a finite number of cases, see Remark 2.3. We also provide new upper bounds of the Hilbert functions of I extending the known bounds for the maximal ideal.

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[3]J. Elias . On the first normalized Hilbert coefficient. J. Pure Appl. Alg. 201 (2005), 116125.

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[6]M. E. Rossi . A bound on the reduction number of a primary ideal. Proc. Amer. Math. Soc. 128 (2000), 13251332.

[7]M. E. Rossi and G. Valla . The Hilbert function of the Ratliff–Rush filtration. J. Pure Appl. Alg. 201 (2005), 2541.

[8]M. E. Rossi , G. Valla and W. V. Vasconcelos . Maximal Hilbert functions. Result. Math. 39 (2001), 99114.

[9]J. Sally and W. V. Vasconcelos . Stable rings. J. Pure Appl. Alg. 4 (1974), 319336.

[10]B. Singh . Effect of a permisible blowing-up on the local Hilbert function. Inv. Math. 26 (1974), 201212.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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