On the existence of an integral normal basis generated by a unit in prime extensions of rational numbers
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- by Stanislav Jakubec, Juraj Kostra and Karol Nemoga PDF
- Math. Comp. 56 (1991), 809-815 Request permission
Abstract:
In the present paper a necessary condition for a cyclic extension of the rationals of prime degree l to have an integral normal basis generated by a unit is given. For a fixed l, this condition implies that there exists at most a finite number of such fields. A computational method for verifying the existence of an integral normal basis generated by a unit is given. For $l = 5$, all such fields are found.References
- Heinrich-Wolfgang Leopoldt, Zur Arithmetik in abelschen Zahlkörpern, J. Reine Angew. Math. 209 (1962), 54–71. MR 139602, DOI 10.1515/crll.1962.209.54
- Philip J. Davis, Circulant matrices, A Wiley-Interscience Publication, John Wiley & Sons, New York-Chichester-Brisbane, 1979. MR 543191
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Math. Comp. 56 (1991), 809-815
- MSC: Primary 11R27; Secondary 11R20
- DOI: https://doi.org/10.1090/S0025-5718-1991-1068814-8
- MathSciNet review: 1068814