Zero-term rank preservers

We obtain characterizations of those linear operators that preserve zero-te rm rank on the m x n matrices over antinegative semirings. That is, a linea r operator T preserves zero-term rank if and only if it has the form T(X) = P(B circle X)Q, where P, Q are permutation matrices and B circle X is the Schur product with B whose entries are all nonzero and not zero-divisors.