  Bosonizations of quantum linear spaces are a large class of pointed Hopf
algebras that include the Taft algebras and their generalizations. We give
conditions for the smash product of an associative algebra with a bosonization
of a quantum linear space to be (semi)prime. These are then used to determine
(semi)primeness of certain smash products with quantum affine spaces. This
extends Bergen's work on Taft algebras.
