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A field extension in which every element satisfies a nonzero polynomial over the base field.
wp-algebraic-extensionmilne-fields-galois-theoryEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Every element of the larger field must satisfy a nonzero polynomial over the base.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
milne-fields-galois-theoryEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Irreducible polynomials with one root in the extension must split there.
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.
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-theory