Let

and

be simply connected CW complexes
with finite rational cohomologies.
The rational toral rank

of a space

is the largest integer

such that the torus

can act continuously
on a CW-complex in the rational homotopy type of

with all its isotropy subgroups finite [8].
As a rational homotopical condition to be a toral map preserving almost free toral actions
for a map

,
we define the rational toral rank

of

, which is a natural invariant
with

for the identity map

of

.
We will see some properties of it by Sullivan models, which is a free commutative differential graded algebra over
Q[4].