  Skew cyclic codes play the same role as cyclic codes in the theory of
error-correcting codes for the rank metric. In this paper, we give descriptions
of these codes by root spaces, cyclotomic spaces and idempotent generators. We
prove that the lattice of skew cyclic codes is anti-isomorphic to the lattice
of root spaces, study these two lattices and extend the rank-BCH bound on their
minimum rank distance to rank-metric versions of the van Lint-Wilson's shift
and Hartmann-Tzeng bounds. Finally, we study skew cyclic codes which are linear
over the base field, proving that these codes include all Hamming-metric cyclic
codes, giving then a new relation between these codes and rank-metric skew
cyclic codes.
