  In the present paper, we study skew cyclic codes over the ring
$F_{q}+vF_{q}+v^2F_{q}$, where $v^3=v,~q=p^m$ and $p$ is an odd prime. We
investigate the structural properties of skew cyclic codes over
$F_{q}+vF_{q}+v^2F_{q}$ using decomposition method. By defining a Gray map from
$F_{q}+vF_{q}+v^2F_{q}$ to $F_{q}^3$, it has been proved that the Gray image of
a skew cyclic code of length $n$ over $F_{q}+vF_{q}+v^2F_{q}$ is a skew
$3$-quasi cyclic code of length $3n$ over $F_{q}$. Further, it is shown that
the skew cyclic codes over $F_{q}+vF_{q}+v^2F_{q}$ are principally generated.
Finally, the idempotent generators of skew cyclic codes over
$F_{q}+vF_{q}+v^2F_{q}$ are also obtained.
