Equivalence Classes of Maximal Orders

Abstract

Introduction, Let k denote the quotient field of a complete discrete rank one valuation ring R. The purpose of this paper is to establish a relationship between the Brauer group of k and the set of maximal orders over R which are equivalent to crossed products over tamely ramified extensions of R.

Ramification Theory for Extensions of Degree p

“…Now Σ Λ(ί? -2i) = -1 mod (p) (see Lemma 2.8 of [7]) we have shown therefore that {β -l) p satisfies an equality of the desired form with « = -1 mod (p,β -l)R [β].…”