In this work, we present a standard model for Galois rings based on the standard model of their residual fields, that is, a sequence of Galois rings starting with ${mathbb Z}_{p^r} that coves all the Galois rings with that characteristic ring and such that there is an algorithm producing each member of the sequence whose input is the size of the required ring.
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.
