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Results tagged with fields
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user 6856
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].
14
votes
Automorphisms of $\mathbb{C}$
There is the more general fact that any automorphism of any subfield of $\mathbb{C}$ can be extended to an automorphism of $\mathbb{C}$. For a proof, see the paper Automorphisms of the Complex Numbers …
- 5,759
1
vote
Separable extensions of henselian fields
The extension $\mathscr{E}\to \mathscr{E}$ induced by $t\mapsto t^p$ is finite separable, but the induced extension of residue fields is $t\mapsto t^p\colon \mathbf{F}_p(\!(t)\!)\to \mathbf{F}_p(\! …
- 5,759
2
votes
2
answers
1k
views
Countable Fields with No Countable Extension
is a partially ordered set under inclusion, and if $K_1\subseteq K_2 \subseteq \cdots$ is an ascending chain of countable subfields, then $\bigcup_{i=1}^{\infty}K_i$ is a countable union of countable fields …
- 5,759