Simple derivations and their images

Ruiyan Sun, Dan Yan

In the paper, we prove that the derivation $D=y{\partial }_x+(a_2(x)y^2+a_1(x)y+a_0(x)){\partial }_y$ of $K[x,y]$ with $a_2(x),a_1(x),a_0(x)\in K[x]$ is simple iff the following conditio…