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Let r be a toric set in the affine space A n k . Given a set of binomials g 1 ,…, g r in the toric ideal P of Γ, we give a criterion for deciding the equality rad(g 1 ,…,g r ) = P. This criterion extends to arbitrary dimension, and to arbitrary fields, an earlier result which concerned only monomial curves over an algebraically closed field of characteristic zero.

On systems of binomials in the ideal of a toric variety