  We study the properties of level zero modules over quantized affine algebras.
The proof of the conjecture on the cyclicity of tensor products by Akasaka and
the present author is given. Several properties of modules generated by
extremal vectors are proved. The weights of a module generated by an extremal
vector are contained in the convex hull of the Weyl group orbit of the
extremalweight. The universal extremal weight module with level zero
fundamental weight as an extremal weight is irreducible, and isomorphic to the
affinization of an irreducible finite-dimensional module.
