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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On the existence of an integral normal basis generated by a unit in prime extensions of rational numbers


Authors: Stanislav Jakubec, Juraj Kostra and Karol Nemoga
Journal: Math. Comp. 56 (1991), 809-815
MSC: Primary 11R27; Secondary 11R20
MathSciNet review: 1068814
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1991-1068814-8
PII: S 0025-5718(1991)1068814-8
Article copyright: © Copyright 1991 American Mathematical Society