Hensel–Shafarevich canonical basis in Lubin–Tate formal modules

In this paper we present a generalization of the Hensel–Shafarevich basis for Lubin–Tate formal modules over a local field. These formal modules are constructed on the maximal ideal of some extension of this field. We study both the case when the extension has perfect residue field and the case with an imperfect residue field.