Monomial preserving derivations and Mathieu-Zhao subspaces

In this paper, we give a complete description of when the image of a monomial preserving derivation (or E-derivation) of the polynomial algebra over a field of characteristic zero is a Mathieu-Zhao subspace. In particular we show that the LFED and LNED conjectures hold for these derivations. The problem of whether the image of a derivation is a Mathieu-Zhao subspace arose from the study of the Jacobian conjecture.