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Equivalence Classes of Maximal Orders

Published online by Cambridge University Press:  22 January 2016

Susan Williamson
Susan Williamson*
Affiliation:
Regis College, Weston, Massachusetts
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Let k denote the quotient field of a complete discrete rank one valuation ring R. The purpose of this paper is to establish a relationship between the Brauer group of k and the set of maximal orders over R which are equivalent to crossed products over tamely ramified extensions of R.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 31 , January 1968 , pp. 131 - 171
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

References

[1] Artin, E., Nesbitt, C. and Thrall, R., Rings with Minimum Condition. Michigan, (1955).Google Scholar
[2] Artin, E. and Tate, J., Class field theory. Princeton notes, 1951. distributed by Harvard Univ.Google Scholar
[3] Auslander, M. and Goldman, O., The Brauer group of a commutative ring, Trans. Amer. Math. Soc. Vol. 97 (1960), pp. 367–409.Google Scholar
[4] Auslander, M. and Goldman, O., Maximal orders, Trans. Amer. Math. Soc. Vol. 97 (1960), pp. 1–24.Google Scholar
[5] Harada, M., Hereditary orders, Trans. Amer. Math. Soc. Vol. 107 (1963), pp. 273–290.Google Scholar
[6] Harada, M., Some criteria for hereditarity of crossed products, Osaka J. Math. Vol. 1 (1964), pp. 69–80 Google Scholar
[7] Serre, J.P., Corps Locaux, Paris, Hermann, (1962).Google Scholar
[8] van der Waerden, B.L., Modern Algebra, Vol. 1, Ungar, (1953).Google Scholar
[9] Weiss, E., Algebraic Number Theory, McGraw-Hill Co., (1963).Google Scholar
[10] Williamson, S., Crossed products and hereditary orders, Nagoya Math. J. Vol. 23 (1963), pp. 103–120.Google Scholar
[11] Williamson, S., Crossed products and maximal orders, Nagoya Math. J. Vol. 25 (1965), pp. 165–174.Google Scholar
[12] Williamson, S., Crossed products and ramification, Nagoya Math. J. Vol. 28 (1966) pp. 85–111.Google Scholar
[13] Brumer, A., The structure of hereditary orders, Ph.D. Thesis, Princeton Univ., (1963).Google Scholar