Image of linear K-derivations and linear ΚƐ-derivations of K[x 1,x 2,x 3,x 4

Abstract

Let K be a field of characteristic zero. We show that the image of a linear K-derivation of rank less than or equal to two over the polynomial algebra is a Mathieu-Zhao subspace. We have further shown that, under certain conditions, the image of -derivations of is a Mathieu-Zhao subspace.