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Results tagged with fields
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user 5513
Fields as algebraic objects. For vector and tensor fields, use eg. [dg.differential-geometry]. For physical fields, use eg. [mp.mathematical-physics] or [quantum-field-theory].
4
votes
Fields whose embeddings into the complex numbers are invariant under complex conjugation
The only fields with this property are algebraic over $\mathbb{Q}$. They are either totally real or a quadratic imaginary extension of a totally real field (but not necessarily finite). … Proof: Note that if a field $L$ satisfies your condition, then any subfield $K$ such that $L/K$ is algebraic also satisfies the condition (embeddings into alg. closed fields can always be extended to embeddings …
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