On the monoid of tame extensions
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- by Cornelius Greither and D. K. Harrison PDF
- Trans. Amer. Math. Soc. 311 (1989), 657-682 Request permission
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.References
- S. U. Chase, D. K. Harrison, and Alex Rosenberg, Galois theory and Galois cohomology of commutative rings, Mem. Amer. Math. Soc. 52 (1965), 15–33. MR 195922
- 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 10.1090/S0002-9947-1986-0860392-3
- D. K. Harrison, Abelian extensions of commutative rings, Mem. Amer. Math. Soc. 52 (1965), 1–14. MR 195921
- Jürgen Neukirch, Klassenkörpertheorie, B. I. Hochschulskripten, vol. 713/713, Bibliographisches Institut, Mannheim-Vienna-Zürich, 1969. MR 0409416
Additional Information
- © Copyright 1989 American Mathematical Society
- 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