  Given $\texttt{S}|\texttt{R}$ a finite Galois extension of finite chain rings
and $\mathcal{B}$ an $\texttt{S}$-linear code we define two Galois operators,
the closure operator and the interior operator. We proof that a linear code is
Galois invariant if and only if the row standard form of its generator matrix
has all entries in the fixed ring by the Galois group and show a Galois
correspondence in the class of $\texttt{S}$-linear codes. As applications some
improvements of upper and lower bounds for the rank of the restriction and
trace code are given and some applications to $\texttt{S}$-linear cyclic codes
are shown.
