Skew cyclic codes over $\mathbb{F}_{q}+v\mathbb{F}_{q}+v^{2}\mathbb{F}_{q}$

In this article, we study skew cyclic codes over ring R = Fq + vFq + v 2 Fq, where q = p, p is an odd prime and v3 = v. We describe generator polynomials of skew cyclic codes over this ring and investigate the structural properties of skew cyclic codes over R by a decomposition theorem. We also describe the generator polynomials of the duals of skew cyclic codes. Moreover, the idempotent generators of skew cyclic codes over Fq and R are considered.