On the ideals of the Radford Hopf algebras.

Let H m , n be the mn²-dimensional Radford Hopf algebra over an algebraically closed field of characteristic zero. In this paper, we show that any finite dimensional indecomposable H m , n -module is a cyclic module. According to the structure of any indecomposable module under the adjoint action of H m , n , we prove that the Radford Hopf algebra H m , n is a principal ideal ring. Furthermore, we give explicitly the generators of all 28 ideals of 9-dimensional Radford Hopf algebra H 1 , 3 . [ABSTRACT FROM AUTHOR]