II-Principal Hereditary Orders

Abstract

Let S denote the integral closure of a complete discrete rank one valuation ring R in a finite Galois extension of the quotient field of R, G the Galois group of the quotient field extension, and f an element of Z2(G,U(S)) where U(S) denotes the multiplicative group of units of S. A crossed product Δ(f, S, G) whose radical is generated as a left ideal by the prime element II of S is an hereditary order according to the Corollary to Thm. 2. 2 of [2], and we call such a crossed product a II-principal hereditary order. In previous papers the author has studied II-principal hereditary orders Δ(f, S, G) for tamely and wildly ramified extensions S of R (see [10] and [11]). The purpose of this paper is to study II-principal hereditary orders Δ(f, S, G) with no restriction on the extension S of R.