  In this work we establish the correspondence between solutions to the
Friedmann--Robertson--Walker cosmologies for perfect fluid and scalar field
sources, where both ones fulfill state equations of the form $p+\rho=\gamma
f(\rho)$, not necessarily linear ones. Such state equations are of common use
in the case of matter--fluids, nevertheless, for a scalar field, they introduce
relationships on the potential and kinetic scalar field energies which restrict
the set of solutions. A theorem on this respect is demonstrated: From any given
(3+1)--cosmological solution, obeying the quoted state equations, one can
derive its (2+1)--cosmological counterpart or vice-versa. Some applications are
given.
