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Totally Imaginary Field


A totally imaginary field is a field with no real embeddings. A general number field K of degree n has s real embeddings (0<=s<=n) and 2t imaginary embeddings (0<=t<=n/2), where n=s+2t. If s=0, K is totally imaginary; if t=0, it is totally real; otherwise it is imaginary but not totally imaginary.


See also

Imaginary Quadratic Field

This entry contributed by David Terr

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Terr, David. "Totally Imaginary Field." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/TotallyImaginaryField.html

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