The Wedderburn-Malcev theorem for comodule algebras

Let H be a Hopf algebra over a field k. Under some assumptions on H we stat e and prove a generalization of the Wedderburn-Malcev theorem for H-comodul e algebras. We show that our Version of this theorem holds for a large enou gh class of Hopf algebras, such as coordinate rings of completely reducible affine algebraic groups, finite dimensional Hopf algebras over fields of c haracteristic 0 and group algebras. Some dual results are also included.