Theorems · Theorem · commutative algebra
Polynomial.residueFieldMapCAlgEquiv_algebraMap
∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) [inst_1 : I.IsPrime] (J : Ideal (Polynomial R)) [inst_2 : J.IsPrime]
[inst_3 : J.LiesOver I] [inst_4 : Algebra (Localization.AtPrime I) (Localization.AtPrime J)]
[inst_5 : Localization.AtPrime.IsLiesOverAlgebra I J] (hJ : J = Ideal.map Polynomial.C I) (p : Polynomial R),
(Polynomial.residueFieldMapCAlgEquiv I J hJ) ((algebraMap (Polynomial R) J.ResidueField) p) =
(algebraMap (Polynomial I.ResidueField) (RatFunc I.ResidueField)) (Polynomial.map (algebraMap R I.ResidueField) p)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
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
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- AlgEquivstatement · cited by 1,681
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- RingHom.compproof · cited by 899
- Ideal.IsPrimestatement and proof · cited by 827
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.residueFieldMapCAlgEquiv_symm_Xproof · cited by 0