Abstract. Let V be an affine toric variety of codimension r over a field of any characteristic. We completely characterize the affine toric varieties that are set-theoretic complete intersections on binomials. In particular we prove that in the characteristic zero case, V is a set-theoretic complete intersection on binomials if and only if V is a complete intersection. Moreover, if F 1 , . . . , Fr are binomials such that . . . , Fr). While in the positive characteristic p case, V is a set-theoretic complete intersection on binomials if and only if V is completely p-glued.These results improve and complete all known results on these topics.

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