  In this paper, we do the two things.
  1. We present a formula to compute the rational cohomology ring of a real
topological toric manifold, and thus that of a small cover or a real toric
manifold, which implies the formula of Suciu and Trevisan. Furthermore, the
formula also works for other coefficient $\mathbb{Z}_q =
\mathbb{Z}/q\mathbb{Z}$, where $q$ is a positive odd integer.
  2. We construct infinitely many real toric manifolds and small covers whose
integral cohomology have a $q$-torsion for any positive odd integer $q$.
