Theorems · Theorem · field theory
Algebra.IsAlgebraic.algHom_bijective
∀ {K : Type u_1} {L : Type u_2} [inst : CommRing K] [IsDomain K] [inst_2 : Field L] [inst_3 : Algebra K L]
[Module.IsTorsionFree K L] [Algebra.IsAlgebraic K L] (f : L →ₐ[K] L), Function.Bijective ⇑f- Defined in
- Mathlib.RingTheory.Algebraic.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Set.Elemproof · cited by 7,166
- Polynomialproof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- AlgHomstatement and proof · cited by 3,236
- IsDomainstatement and proof · cited by 2,196
- Function.Bijectivestatement · cited by 863
- Polynomial.mapproof · cited by 806
- Polynomial.aevalproof · cited by 615
Cited by4
Results whose statement or proof uses this declaration.
- Algebra.IsAlgebraic.algEquivEquivAlgHomproof · cited by 5
- Algebra.IsAlgebraic.algHom_bijective₂proof · cited by 4
- FiniteField.frobeniusAlgEquivOfAlgebraic_symm_applystatement · cited by 0
- Algebra.IsAlgebraic.algEquivEquivAlgHom_symm_applystatement · cited by 0