Theorems · Theorem · field theory
Algebra.isSeparable_of_separable_splitting_field
∀ (F : Type u) (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] {p : Polynomial F}
[sp : Polynomial.IsSplittingField F E p], p.Separable → Algebra.IsSeparable F EIf p is a separable polynomial with splitting field E over F, then E / F is a
separable extension.
- Defined in
- Mathlib.FieldTheory.SeparableClosure
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- IntermediateFieldproof · cited by 988
- Algebra.IsSeparablestatement and proof · cited by 210
- Polynomial.Separablestatement and proof · cited by 117
- Polynomial.rootSetproof · cited by 101
- Polynomial.IsSplittingFieldstatement and proof · cited by 50
- minpoly.dvdproof · cited by 31
- Polynomial.Separable.of_dvdproof · cited by 14
- IntermediateField.isSeparable_adjoin_iff_isSeparableproof · cited by 4
- Polynomial.aeval_eq_zero_of_mem_rootSetproof · cited by 3
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