Theorems · Theorem · commutative algebra
IsLocalization.AtPrime.under_map_of_isMaximal
∀ {R : Type u_1} [inst : CommSemiring R] (S : Type u_2) [inst_1 : CommSemiring S] [inst_2 : Algebra R S] (p : Ideal R)
[inst_3 : p.IsPrime] (Sₚ : Type u_5) [inst_4 : CommSemiring Sₚ] [inst_5 : Algebra S Sₚ]
[IsLocalization (Algebra.algebraMapSubmonoid S p.primeCompl) Sₚ] (P : Ideal S) [P.IsMaximal] [P.LiesOver p],
Ideal.under S (Ideal.map (algebraMap S Sₚ) P) = P- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · 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.mapstatement · cited by 692
- IsLocalizationstatement and proof · cited by 636
- Ideal.primeComplstatement and proof · cited by 462
- Ideal.IsMaximalstatement and proof · cited by 452
- Ideal.LiesOverstatement and proof · cited by 272
- Ideal.understatement · cited by 170
Cited by1
Results whose statement or proof uses this declaration.
- IsLocalization.AtPrime.comap_map_of_isMaximalproof · cited by 0