Archiv der Mathematik

, Volume 74, Issue 1, pp 22–25

On the binomial arithmetical rank

  • A. Thoma

DOI: 10.1007/PL00000405

Cite this article as:
Thoma, A. Arch. Math. (2000) 74: 22. doi:10.1007/PL00000405


The binomial arithmetical rank of a binomial ideal I is the smallest integer s for which there exist binomials f1,..., fs in I such that rad (I) = rad (f1,..., fs). We completely determine the binomial arithmetical rank for the ideals of monomial curves in \(P_K^n\). In particular we prove that, if the characteristic of the field K is zero, then bar (I(C)) = n - 1 if C is complete intersection, otherwise bar (I(C)) = n. While it is known that if the characteristic of the field K is positive, then bar (I(C)) = n - 1 always.

Copyright information

© Birkhäuser Verlag, Basel 2000

Authors and Affiliations

  • A. Thoma
    • 1
  1. 1.Department of Mathematics, University of Ioannina, 45110 Ioannina, GreeceGR

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