ON CYCLIC FIELD-EXTENSIONS OF DEGREE-8

A 6-parameter family of cyclic extensions of degree 8 is given over any field. This family parametrizes all C-8 extensions over a number of fields including Q, any field containing square-root 2 or square-root -1, all number fields having a single prime over 2, all local fields whose residue field has characteristic different from 2 and all these fields with any number of indeterminates adjoined.