Theorems · Theorem · field theory
IntermediateField.restrictRestrictAlgEquivMapHom_surjective
∀ {F : Type u_1} {E : Type u_2} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] (K L : IntermediateField F E)
[inst_3 : Normal F ↥K] [FiniteDimensional F ↥K] [FiniteDimensional (↥L) E] [IsGalois (↥L) E],
K ⊓ L = ⊥ → Function.Surjective ⇑(IntermediateField.restrictRestrictAlgEquivMapHom F (↥K) (↥L) E)- Defined in
- Mathlib.FieldTheory.Galois.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Bot.botstatement and proof · cited by 4,720
- Algebra.algebraMapproof · cited by 4,706
- MonoidHomstatement · cited by 3,629
- FiniteDimensionalstatement and proof · cited by 1,854
- AlgEquivstatement and proof · cited by 1,681
- IntermediateFieldstatement and proof · cited by 988
- AlgHom.toRingHomproof · cited by 490
- MonoidHom.rangeproof · cited by 314
- Algebra.ofIdproof · cited by 166
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