On the binomial arithmetical rank
- Cite this article as:
- Thoma, A. Arch. Math. (2000) 74: 22. doi:10.1007/PL00000405
- 88 Downloads
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.