  We discuss the Freund-Rubin compactification with cosmological constant and
the dilaton field, and examine the stability of the spacetimes at the low
energy. The Minkowski or de Sitter spacetime can be obtained if the dilation
field is turned off while we observe that the dilaton field does not permit
such spacetimes but only the anti-de Sitter spacetime. The stability of the
spacetime depends on the dimensions of the spacetime and the compactified space
and the coupling constant of the dilaton field $a$. In the $a=1$ case, which
corresponds to superstring theories, the anti-de Sitter vacuum is stable at
least in the linear level.
