Theorems · Theorem · field theory
IntermediateField.algHomEquivAlgHomOfSplits_symm_apply
∀ {F : Type u_1} {K : Type u_2} (A : Type u_3) [inst : Field F] [inst_1 : Field K] [inst_2 : Field A]
[inst_3 : Algebra F K] [inst_4 : Algebra F A] [inst_5 : Algebra.IsAlgebraic F K] (L : IntermediateField F A)
(hL : ∀ (x : K), (Polynomial.map (algebraMap F ↥L) (minpoly F x)).Splits) (f : K →ₐ[F] A),
(IntermediateField.algHomEquivAlgHomOfSplits A L hL).symm f = f.codRestrict L.toSubalgebra ⋯- Defined in
- Mathlib.FieldTheory.IsAlgClosed.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
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- DFunLike.coestatement and proof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- Equivstatement · cited by 8,337
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapstatement and proof · cited by 4,706
- Equiv.symmstatement and proof · cited by 3,681
- AlgHomstatement and proof · cited by 3,236
- Subalgebrastatement · cited by 1,353
- IntermediateFieldstatement and proof · cited by 988
- Polynomial.mapstatement and proof · cited by 806
- minpolystatement and proof · cited by 439
- Algebra.IsAlgebraicstatement and proof · cited by 322
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