II -Principal Hereditary Orders

Source 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 Z 2 ( 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 .