  The aim of this paper is to give conditions for the equivalency between skew
constacyclic codes, skew cyclic codes and skew negacyclic codes defined over
semi-local rings. Also, we provide construction and an enumeration of Euclidean
and Hermitian skew LCD cyclic codes over $ \mathbb{F}_{p^{t}}+ v
\mathbb{F}_{p^{t}} $. Several optimal LCD codes are obtained from Gray images
of LCD skew codes over semi-local rings.
