Cyclic extensions of

Authors:
Jón Kr. Arason, Burton Fein, Murray Schacher and Jack Sonn

Journal:
Trans. Amer. Math. Soc. **313** (1989), 843-851

MSC:
Primary 12F10; Secondary 11R20

MathSciNet review:
929665

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Abstract: In this paper the height of a cyclic -extension of a field of characteristic is studied. Here means that there is a cyclic extension of , with . Necessary and sufficient conditions are given for provided contains a primitive th root of unity. Primary emphasis is placed on the case . Suppose . It is shown that and if is a number field then for all . For each an example is given of a field such that but .

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DOI:
http://dx.doi.org/10.1090/S0002-9947-1989-0929665-2

Article copyright:
© Copyright 1989
American Mathematical Society