  We study the generalization of the S\'aez-Ballester theory applied to a flat
FRW cosmological model. Classical exact solutions up to quadratures are easily
obtained using the Hamilton-Jacobi approach. Contrary to claims in the
specialized literature, it is shown that the S\'aez-Ballester theory cannot
provide a realistic solution to the dark matter problem of Cosmology.
Furthermore the quantization procedure of the theory can be simplified by
reinterpreting the theory in the Einstein frame, where the scalar field can be
interpreted as part of the matter content of the theory, in this approach,
exact solutions are also found for the Wheeler-DeWitt equation in the quantum
regime.
