Generators of the group of principal units of a cyclic p-extension of a regular local field

TLDR: In this article, Borevich showed that Λ-module E has a system of n+1 generators, of which n−1 are free and two are connected by certain relations.

Abstract: Suppose k is a local field that is an extension of the field of p -adic numbers of degree n and does not contain a primitive p -th root of 1, and suppose K/k is a cyclic p-extension with Galois group G. The group E of principal units of K is a multiplicatively written module over the group ring Λ=ℤp[G], where ℤp is the ring of p-adic integers. It was shown by Borevich (Ref. Zh. Mat., 1965, 3A256) that the Λ-module E has a system of n+1 generators, of which n−1 are free and two are connected by certain relations. In the present paper these Λ-generators are constructed explicitly and their arithmetical characteristics indicated.