On the module structure of a p-extension over a -adic number field

Abstract

Throughout this paper, let p be an odd prime. Let k be a -adic number field and be the ring of all integers in k. Let K/k be a finite totally ramified Galois p-extension of degree pn with the Galois group G. Clearly the ring of all integers in K is an [G]-module. In the previous paper [4], we studied [G]-module structure of in a cyclic totally ramified p-extension, and we have obtained the condition for to be an indecomposable [G]-module.