Theorems · Definition · field theory
RatFunc.IntermediateField.adjoinXEquiv
{K : Type u_1} → [inst : Field K] → (E : IntermediateField K (RatFunc K)) → ↥(↥E)⟮RatFunc.X⟯ ≃ₐ[↥E] RatFunc KThe equivalence between E⟮X⟯ and K⟮X⟯ as E-algebras.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Fieldstatement and proof · cited by 7,404
- AlgEquivstatement · cited by 1,681
- IntermediateFieldstatement and proof · cited by 988
- IntermediateField.adjoinstatement · cited by 382
- RatFuncstatement and proof · cited by 301
- AlgEquiv.transproof · cited by 108
- RatFunc.Xstatement · cited by 58
- IntermediateField.topEquivproof · cited by 24
- IntermediateField.equivOfEqproof · cited by 13
- RatFunc.IntermediateField.adjoin_Xproof · cited by 0
Cited by2
Results whose statement or proof uses this declaration.
- RatFunc.finrank_eq_max_natDegreeproof · cited by 1
- RatFunc.isAlgebraic_adjoin_simple_X'proof · cited by 0