Field theory and polynomials Galois theory Concept
Galois extension
Summary
A Galois extension is an algebraic field extension that is normal and separable. Galois extensions are the extensions to which the fundamental theorem of Galois theory applies. The definition of a Galois extension states it.
Where this leads
13 pages build on this one.
Further reading
- Web https://en.wikipedia.org/wiki/Galois_extension, lead section
About this page
| Tag | 0QMZAQ6QQ4 |
|---|---|
| URI | m2://0QMZAQ6QQ4 |
| Kind | concept |
| Writing | W1 stated |
| MSC | 12F10 |
| Specializes | Normal extension, Separable extension |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
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What links here
Definitions
Used by
- Kummer theory
- Splitting of prime ideals
- Artin reciprocity law
- Class field theory
- Kronecker–Weber theorem
- Hilbert class field
- Iwasawa theory
- Decomposition group
- Frobenius element
- Crossed product algebra
- Fundamental identity for ramification and inertia
- Chebotarev's density theorem
- Ramification group