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II-Principal Hereditary Orders

Published online by Cambridge University Press:  22 January 2016

Susan Williamson
Susan Williamson*
Affiliation:
Regis College, Weston, Massachusetts
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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.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 32 , June 1968 , pp. 41 - 65
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

References

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