Mathieu Subspaces of Univariate Polynomial Algebras

Arno van den Essen, Wenhua Zhao

Published 2010-12-09Version 1

We first give a characterization for Mathieu subspaces of univariate polynomial algebras over fields in terms of their radicals. We then deduce that for some classes of classical univariate orthogonal polynomials the Image Conjecture is true. We also prove two special cases of the one-dimensional Image Conjecture for univariate polynomial algebras $A[t]$ over commutative $\Bbb Q$-algebras $A$.