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Crossed Products and Hereditary Orders

Published online by Cambridge University Press:  22 January 2016

Susan Williamson
Susan Williamson*
Affiliation:
Brandeis University, Waltham, Massachusetts
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Let S be the integral closure of a discrete rank one valuation ring R in a finite Galois extension of the quotient field of R, and denote the Galois group of the quotient field extension by G. It has been proved by Auslander and Rim in [4] that the trivial crossed product Δ(l, S, G) is an hereditary order for tamely ramified extensions S of R and that Δ(l, S, G) is a maximal order if and only if S is an unramified extension of R. The purpose of this paper is to study the crossed product Δ(f, S, G) where [f] is any element of H2(G, U(S)) and S is a tamely ramified extension of R with multiplicative group of units U(S).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 23 , December 1963 , pp. 103 - 120
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1963

References

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