Mathieu-Zhao spaces of polynomial rings

Abstract

We describe all Mathieu-Zhao spaces of $k[x_1,\cdots ,x_n]$ ($k$ is an algebraically closed field of characteristic zero) which contains an ideal of finite codimension. Furthermore we give an algorithm to decide if a subspace of the form $I+k{v}_1+\cdots +k{v}_r$ is a Mathieu-Zhao space, in case the ideal $I$ has finite codimension.

Latex 10 pages