Abstract.
The binomial arithmetical rank of a binomial ideal I is the smallest integer s for which there exist binomials f 1,..., f s in I such that rad (I) = rad (f 1,..., f s). 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.
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Received: 9.10.1998
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Thoma, A. On the binomial arithmetical rank. Arch. Math. 74, 22–25 (2000). https://doi.org/10.1007/PL00000405
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DOI: https://doi.org/10.1007/PL00000405