Theorems · Definition · field theory
AlgebraicIndependent.aevalEquivField
{ι : Type u_1} →
{F : Type u_2} →
{E : Type u_3} →
{x : ι → E} →
[inst : Field F] →
[inst_1 : Field E] →
[inst_2 : Algebra F E] →
AlgebraicIndependent F x →
FractionRing (MvPolynomial ι F) ≃ₐ[F] ↥(IntermediateField.adjoin F (Set.range x))Canonical isomorphism between rational function field and the intermediate field generated by algebraically independent elements.
- Cited by
- 5 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.
Cites17
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
- Finsuppstatement · cited by 5,255
- Set.rangestatement · cited by 4,705
- AlgHomproof · cited by 3,236
- MvPolynomialstatement and proof · cited by 2,140
- AlgEquivstatement and proof · cited by 1,681
- IntermediateFieldstatement · cited by 988
- nonZeroDivisorsstatement · cited by 895
- IntermediateField.adjoinstatement · cited by 382
- FractionRingstatement and proof · cited by 200
- AlgebraicIndependentstatement and proof · cited by 120
Cited by6
Results whose statement or proof uses this declaration.
- AlgebraicIndependent.reprFieldproof · cited by 2
- IsTranscendenceBasis.lift_rank_eq_max_liftproof · cited by 1
- AlgebraicIndependent.lift_reprFieldproof · cited by 1
- AlgebraicIndependent.aevalEquivField.congr_simpstatement and proof · cited by 0
- AlgebraicIndependent.aevalEquivField_algebraMap_apply_coestatement · cited by 0
- AlgebraicIndependent.aevalEquivField_apply_coestatement · cited by 0