On the Hilbert coefficients and reduction numbers

How to Cite

Tan TTQ. On the Hilbert coefficients and reduction numbers. HueUni-JNS [Internet]. 2020Jun.30 [cited 2021Mar.9];129(1D):67-70. Available from: http://jos.hueuni.edu.vn/index.php/HUJOS-NS/article/view/5803


Let (R, m) be a nonetherian local ring with dim(R) = d ≥ 1 and depth(R) ≥ d − 1. Let I be an m-primary ideal of R. In this paper, we study the non-positivity of the Hilbert coefficients ei(I) under some conditions.



  1. Mandal M, Singh B, Verma JK. On some conjectures about the Chern numbers of filtration. Journal of Algebra. 2011;325(1):147-162.
  2. McCune L. Hilbert coefficients of parameter ideals, J Commutative Algebra. 2013;5(3):399-412.
  3. Saikia A, Saloni K. Bounding Hilbert coefficients of parameter ideals. Journal of Algebra. 2018;501 (1):328-344.
  4. Linh CH, Trung VD. Hilbert coefficients and the depth of associated graded rings. Vietnam Journal of Mathematics. 2019;47(2):431-442.
  5. Puthenpurakal TJ. Ratliff-Rush filtration, regularity and depth of higher associated graded modules Part II. Journal of Pure and Applied Algebra. 2017; 221 (3):611-631.
  6. Rossi ME, Valla G. Hilbert Functions of Filtered Modules. Vol 9. Berlin (DE): Springer-Verlag Berlin Heidelberg; 2010. 100 p.
  7. Trung NV. Reduction exponent and degree bound for the defining equations of graded rings. Proceedings of the American Mathematical Society. 1987;101(2):229-236.
  8. Elias J. Depth of higher associated graded rings. Journal London Mathematical Society. 2004;70(1): 41-58.
  9. Hoa LT. Reduction numbers and Rees algebra of powers of an ideal. Proceedings of the American Mathematical Society. 1993;119(2):415-422.
  10. Linh CH . Bounds for Hilbert coefficients. Viasm: Preprint_1913 [Preprint]. 2019.
  11. Blancafort C. On Hilbert functions and cohomology. Journal of Algebra. 1997;192(1):439-459.
  12. Hoa LT. Reduction numbers of equimultiple ideals. Journal of Pure and Applied Algebra. 1996;109 (2):111-126.
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