Theorems · Theorem · commutative algebra
Localization.localRingHom_bijective_of_saturated_inf_eq_top
∀ {R : Type u_1} [inst : CommSemiring R] (S : Type u_2) [inst_1 : CommSemiring S] [inst_2 : Algebra R S] {P : Ideal S}
[inst_3 : P.IsPrime] {s : Subalgebra R S},
s.saturation (P.primeCompl ⊓ s.toSubmonoid) ⋯ = ⊤ →
∀ (p : Ideal ↥s) [inst_4 : p.IsPrime] [inst_5 : P.LiesOver p],
Function.Bijective ⇑(Localization.localRingHom p P (algebraMap (↥s) S) ⋯)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites39
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
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Top.topstatement and proof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- Submonoidstatement · cited by 3,086
- Nat.cast_oneproof · cited by 2,501
- mul_assocproof · cited by 1,667
- Subalgebrastatement and proof · cited by 1,353
Cited by1
Results whose statement or proof uses this declaration.
- Localization.localRingHom_bijective_of_not_conductor_leproof · cited by 0