  We study the finite dimensional modules on the half-quantum group u_q^+ at a
root of unity q, whose action can be extended to u_q (quotient of the quantized
enveloping algebra of sl_2). We derive decomposition formulas of the tensor
product of indecomposable u_q^+-modules, which includes the cases of the
universal and the quantized universal enveloping algebra of sl_2 for q not a
root of unity. We also prove that simple modules on u_q correspond exactly to
the extendable non projective u_q^+-modules. We thus establish decomposition
formulas for the tensor product of simple u_q-modules.
