Theorems · Theorem · field theory
AlgHom.algebraicIndependent_iff
∀ {ι : Type u} {R : Type u_2} {A : Type v} {A' : Type v'} {x : ι → A} [inst : CommRing R] [inst_1 : CommRing A]
[inst_2 : CommRing A'] [inst_3 : Algebra R A] [inst_4 : Algebra R A'] (f : A →ₐ[R] A'),
Function.Injective ⇑f → (AlgebraicIndependent R (⇑f ∘ x) ↔ AlgebraicIndependent R x)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- AlgHomstatement and proof · cited by 3,236
- Function.Injective.injOnproof · cited by 280
- AlgebraicIndependentstatement and proof · cited by 120
- AlgebraicIndependent.of_compproof · cited by 3
- AlgebraicIndependent.mapproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- IsTranscendenceBasis.of_compproof · cited by 2