Theorems · Theorem · commutative algebra
IsLocalization.AtPrime.under_map_eq_map
∀ {S : Type u_6} {R : Type u_7} [inst : CommRing R] (p : Ideal R) [inst_1 : p.IsMaximal] {Sₚ : Type u_9}
[inst_2 : CommRing S] [inst_3 : Algebra R S] [inst_4 : CommRing Sₚ] [inst_5 : Algebra S Sₚ] [inst_6 : Algebra R Sₚ]
[IsLocalization (Algebra.algebraMapSubmonoid S p.primeCompl) Sₚ] [IsScalarTower R S Sₚ],
Ideal.under S (Ideal.map (algebraMap R Sₚ) p) = Ideal.map (algebraMap R S) p- Cited by
- 1 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites43
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement and proof · cited by 10,189
- SetLike.coeproof · cited by 8,199
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- HasQuotient.Quotientproof · cited by 2,301
- mul_commproof · cited by 2,262
- mul_assocproof · cited by 1,667
- one_smulproof · cited by 1,374
Cited by1
Results whose statement or proof uses this declaration.
- IsLocalization.AtPrime.comap_map_eq_mapproof · cited by 0