  We define left and right kernels of representations of Hopf algebras. In the
case of group algebras, left and right kernels coincide and they are the usual
kernels of modules. In the general case we show that these kernels coincide
with the categorical left and right Hopf kernels of morphisms of Hopf algebras
defined in \cite{AD}. Brauer's theorem for kernels over group algebras is
generalized to Hopf algebras.
