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An algebraic extension in which every element has a separable minimal polynomial over the base field.
wp-separable-extensionnlab-separable-extensionmilne-fields-galois-theoryEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Minimal polynomials must have distinct roots in a splitting field.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
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-theoryEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Supply separability of the same algebraic extension as the other jointly required input.
Feed several structures into a construction junction and impose compatibility between them.
milne-fields-galois-theory