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An algebraic extension that is both normal and separable.
wp-galois-extensionnlab-galois-extensionmilne-fields-galois-theoryEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
An algebraic extension that is both normal and separable is Galois.
Feed several structures into a construction junction and impose compatibility between them.
milne-fields-galois-theoryEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Finite Galois extensions have an inclusion-reversing subgroup–intermediate-field correspondence.
Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.
milne-fields-galois-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
The automorphisms of fixing form .
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
milne-fields-galois-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
A Galois extension is normal and separable; forgetting separability leaves a normal extension.
Pass canonically from a stronger object to structure it determines, or forget part of the data while retaining a valid weaker structure. The carrier may change under a canonical induced construction.
milne-fields-galois-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
A Galois extension is normal and separable; forgetting normality leaves a separable extension.
Pass canonically from a stronger object to structure it determines, or forget part of the data while retaining a valid weaker structure. The carrier may change under a canonical induced construction.
milne-fields-galois-theory