Steinitz classes in quartic fields
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- by Stephen Pierce PDF
- Proc. Amer. Math. Soc. 43 (1974), 39-41 Request permission
Abstract:
Let $K$ be normal quartic over the rationals. Let $l \equiv 3$ (4) be an odd prime. If the class number of $K$ is even, there is a normal extension $L$ of degree $l$ over $K$ such that the relative discriminant is principal, but $L$ has no relative integral base over $K$.References
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E. Artin, Collected works, Addison-Wesley, Reading, Mass., pp. 229-321.
- A. Fröhlich, The discriminants of relative extensions and the existence of integral bases, Mathematika 7 (1960), 15–22. MR 151451, DOI 10.1112/S0025579300001534 H. Hasse, Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebrasichen Zahlkörper, 1930.
- Henry B. Mann, On integral bases, Proc. Amer. Math. Soc. 9 (1958), 167–172. MR 93502, DOI 10.1090/S0002-9939-1958-0093502-7
- Robert L. Long, Steinitz classes of cyclic extensions of prime degree, J. Reine Angew. Math. 250 (1971), 87–98. MR 289457, DOI 10.1515/crll.1971.250.87
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 43 (1974), 39-41
- MSC: Primary 12A30
- DOI: https://doi.org/10.1090/S0002-9939-1974-0327715-2
- MathSciNet review: 0327715