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Crossed Products and Maximal Orders

Published online by Cambridge University Press:  22 January 2016

Susan Williamson
Susan Williamson*
Affiliation:
Harvard University, Cardinal Gushing College
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Let I’ be a maximal order over a complete discrete rank one valuation ring R in a central simple algebra over the quotient field of R. The purpose of this paper is to determine necessary and sufficient conditions for I’ to be equivalent to a crossed product over a tamely ramified extension of R.

It is a classical result that every central simple algebra over a field k is equivalent to a crossed product over a Galois extension of k. Furthermore, it has been proved by Auslander and Goldman in [2] that every central separable algebra over a local ring is equivalent to a crossed product over an unramified extension.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 25 , 1965 , pp. 165 - 174
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1965

References

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