Theorems · Definition · commutative algebra
Polynomial.Bivariate.Transcendental.algEquivAdjoin
{R : Type u_1} →
{A : Type u_2} →
[inst : CommRing R] →
[inst_1 : Ring A] →
[inst_2 : Algebra R A] → {x : A} → Transcendental R x → Polynomial (Polynomial R) ≃ₐ[R] Polynomial ↥R[x]The AlgEquiv between R[X][Y] and R[a][Y] for some transcendental a.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
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
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Polynomialstatement · cited by 5,681
- AlgEquivstatement · cited by 1,681
- Subalgebrastatement · cited by 1,353
- Algebra.adjoinstatement · cited by 535
- Transcendentalstatement and proof · cited by 91
- Polynomial.algEquivOfTranscendentalproof · cited by 11
- Polynomial.mapAlgEquivproof · cited by 7
Cited by5
Results whose statement or proof uses this declaration.
- Polynomial.Bivariate.Transcendental.algEquivAdjoin_swap_eq_aevalstatement · cited by 1
- IsAlgebraic.adjoin_singletonproof · cited by 1
- Polynomial.Bivariate.aeval_aeval_eq_aeval_algEquivAdjoinstatement and proof · cited by 1
- Polynomial.Bivariate.Transcendental.algEquivAdjoin_applystatement · cited by 0
- Polynomial.Bivariate.Transcendental.algEquivAdjoin.congr_simpstatement and proof · cited by 0