When " K " has characteristic 2, there are no such Kummer extensions.
2.
The Kummer extensions in this case also include "'biquadratic extensions "'and more general "'multiquadratic extensions " '.
3.
Taking " n " = 3, there are no degree 3 Kummer extensions of the rational number field "'Q "', since for three cube roots of 1 complex numbers are required.
4.
When the extension is abelian and the order of vanishing of an L-function at " s " = 0 is one, Stark's refined conjecture predicts the existence of the Stark units, whose roots generate Kummer extensions of " K " that are abelian over the base field " k " ( and not just abelian over " K ", as Kummer theory implies ).
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