On the monoid of tame extensions
Authors:
Cornelius Greither and D. K. Harrison
Journal:
Trans. Amer. Math. Soc. 311 (1989), 657-682
MSC:
Primary 11R33
DOI:
https://doi.org/10.1090/S0002-9947-1989-0978371-7
MathSciNet review:
978371
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Abstract: This paper deals with not necessarily maximal orders in abelian extensions of number fields. We restrict our attention to orders invariant under the Galois group $G$. Based on recent work of Childs and Hurley [CH], we introduce a notion of tameness for such orders (actually this is done in a slightly more general setting). The maximal order is tame in this sense if and only if the field extension is tamely ramified.
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- Lindsay N. Childs and Susan Hurley, Tameness and local normal bases for objects of finite Hopf algebras, Trans. Amer. Math. Soc. 298 (1986), no. 2, 763–778. MR 860392, DOI https://doi.org/10.1090/S0002-9947-1986-0860392-3
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- Jürgen Neukirch, Klassenkörpertheorie, Bibliographisches Institut, Mannheim-Vienna-Zürich, 1969. B. I-Hochschulskripten, 713/713a*. MR 0409416
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© Copyright 1989
American Mathematical Society