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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 $\alpha$-constacycliccodes are either equivalent to $\alpha$-constacyclic codes or$\alpha$-quasi-twisted codes over $\mathcal{R}$. Further, structuralproperties, specially, generating polynomials and idempotent generators forskew cyclic and skew constacyclic codes are determined by decomposition method.

Skew cyclic and skew $(\alpha_1 + u\alpha_2 + v\alpha_3 + uv\alpha_4)$-constacyclic codes over $F_q + uF_q + vF_q + uvF_q$