Theorems · Theorem · commutative algebra
Localization.localRingHom_unique
∀ {R : Type u_1} [inst : CommSemiring R] {P : Type u_3} [inst_1 : CommSemiring P] (I : Ideal R) [hI : I.IsPrime]
(J : Ideal P) [inst_2 : J.IsPrime] (f : R →+* P) (hIJ : I = Ideal.comap f J)
{j : Localization.AtPrime I →+* Localization.AtPrime J},
(∀ (x : R), j ((algebraMap R (Localization.AtPrime I)) x) = (algebraMap P (Localization.AtPrime J)) (f x)) →
Localization.localRingHom I J f hIJ = j- Cited by
- 3 results in Mathlib
- Foundations
- Depth 65 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.
- DFunLike.coestatement and proof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement and proof · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.primeComplstatement · cited by 462
- Ideal.comapstatement and proof · cited by 443
- Localization.AtPrimestatement and proof · cited by 299
- Localization.localRingHomstatement · cited by 54
- IsLocalization.map_uniqueproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Localization.localRingHom_compproof · cited by 5
- Localization.localRingHom_idproof · cited by 3
- AlgebraicGeometry.localRingHom_comp_stalkIsoproof · cited by 3