Cyclic quartic fields with relative integral bases over their quadratic subfields
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- by Blair K. Spearman and Kenneth S. Williams
- Proc. Amer. Math. Soc. 103 (1988), 687-694
- DOI: https://doi.org/10.1090/S0002-9939-1988-0947640-3
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Abstract:
Explicit conditions are given for a cyclic quartic field to have a relative integral basis over its unique quadratic subfield.References
- Robert H. Bird and Charles J. Parry, Integral bases for bicyclic biquadratic fields over quadratic subfields, Pacific J. Math. 66 (1976), no. 1, 29–36. MR 432592
- Hugh M. Edgar, A number field without any integral basis, Math. Mag. 52 (1979), no. 4, 248–251. MR 545571, DOI 10.2307/2689423
- Kenneth Hardy, R. H. Hudson, D. Richman, Kenneth S. Williams, and N. M. Holtz, Calculation of the class numbers of imaginary cyclic quartic fields, Math. Comp. 49 (1987), no. 180, 615–620. MR 906194, DOI 10.1090/S0025-5718-1987-0906194-5
- R. H. Hudson and K. S. Williams, The integers of a cyclic quartic field, Rocky Mountain J. Math. 20 (1990), no. 1, 145–150. MR 1057983, DOI 10.1216/rmjm/1181073167
- Robert MacKenzie and John Scheuneman, A number field without a relative integral basis, Amer. Math. Monthly 78 (1971), 882–883. MR 288094, DOI 10.2307/2316485
- Henry B. Mann, On integral bases, Proc. Amer. Math. Soc. 9 (1958), 167–172. MR 93502, DOI 10.1090/S0002-9939-1958-0093502-7 I. Niven and H. S. Zuckerman, An introduction to the theory of numbers, 2nd ed., Wiley, 1968.
- Zhang Xianke, Cyclic quartic fields and genus theory of their subfields, J. Number Theory 18 (1984), no. 3, 350–355. MR 746869, DOI 10.1016/0022-314X(84)90067-2
Bibliographic Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 687-694
- MSC: Primary 11R16; Secondary 11R33
- DOI: https://doi.org/10.1090/S0002-9939-1988-0947640-3
- MathSciNet review: 947640