Let L/K be a finite, Galois extension of local or global fields. In the classical setting of additive Galois modules, the ring of integers O L of L is studied as a module for the group ring O K G, where G is the Galois group of L/K. When K is a p-adic field, we also find a structure of O K G module when we replace O L with the group of points in O L of a Lubin-Tate formal group defined over K. For this new Galois module we find an analogue of the normal basis theorem. When K is a proper unramified extension of Q p , we show that some eigenspaces for the Teichmüller character are not free. We also adapt certain cases of E. Noether’s result on normal integral bases for tame extensions. Finally, for wild extensions we define a version of Leopoldt’s associated order and demonstrate in a specific case that it is strictly larger than the integral group ring.