  In this note, we study skew cyclic and skew constacyclic codes over the ring
$\mathcal{R}=F_{q}+uF_{q}+vF_{q}+uvF_{q}$ where $q=p^{m},$ $p$ is an odd prime,
$u^{2}=u,~v^{2}=v,~uv=vu$. We show that Gray images of a skew cyclic and skew
$\alpha$-constacyclic code of length $n$ are skew quasi-cyclic code of length
$4n$ over $F_{q}$ of index 4. Also, it is shown that skew $\alpha$-constacyclic
codes are either equivalent to $\alpha$-constacyclic codes or
$\alpha$-quasi-twisted codes over $\mathcal{R}$. Further, structural
properties, specially, generating polynomials and idempotent generators for
skew cyclic and skew constacyclic codes are determined by decomposition method.
