Explicit conditions are given for a cyclic quartic field to have a relative integral basis over its unique quadratic subfield.

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Keywords Cyclic quartic field, Relative different and discriminant, Relative integral basis
Persistent URL dx.doi.org/10.1090/S0002-9939-1988-0947640-3
Journal Proceedings of the American Mathematical Society
Spearman, B.K. (Blair K.), & Williams, K.S. (1988). Cyclic quartic fields with relative integral bases over their quadratic subfields. Proceedings of the American Mathematical Society, 103(3), 687–694. doi:10.1090/S0002-9939-1988-0947640-3