Steinitz classes in quartic fields
Author:
Stephen Pierce
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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Let 
be normal quartic over the rationals. Let 
(4) be an odd prime. If the class number of 
is even, there is a normal extension 
of degree 
over 
such that the relative discriminant is principal, but 
has no relative integral base over 
.
- [1] E. Artin, Collected works, Addison-Wesley, Reading, Mass., pp. 229-321.
- [2] A. Fröhlich, The discriminants of relative extensions and the existence of integral bases, Mathematika 7 (1960), 15–22. MR 151451, https://doi.org/10.1112/S0025579300001534
- [3] H. Hasse, Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebrasichen Zahlkörper, 1930.
- [4] Henry B. Mann, On integral bases, Proc. Amer. Math. Soc. 9 (1958), 167–172. MR 93502, https://doi.org/10.1090/S0002-9939-1958-0093502-7
- [5] Robert L. Long, Steinitz classes of cyclic extensions of prime degree, J. Reine Angew. Math. 250 (1971), 87–98. MR 289457, https://doi.org/10.1515/crll.1971.250.87
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 12A30
Retrieve articles in all journals with MSC: 12A30
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1974-0327715-2
Keywords:
Steinitz class,
ideal class group
Article copyright:
© Copyright 1974
American Mathematical Society
