  We investigated the representation thoery of an Ariki-Koike algebra whose
Poincare polynomial associated with the "bottom", i.e., the subgroup on which
the symmetric group acts, is non-zero in the base field. We proved that the
module category of such an Ariki-Koike algebra is Morita equivalent to the
module category of a direct sum of tensor products of Hecke algebras associated
with certain symmetric groups. We also generalized this Morita equivalence
theorem to give a Morita equivalenve between a $q$-Schur$^m$ algebra and a
direct sum of tensor products of certain $q$-Schur algebras.
