Theorems · Theorem · commutative algebra
Algebra.FormallySmooth.localization_base
∀ {R : Type u_4} {Rₘ : Type u_6} {Sₘ : Type u_7} [inst : CommRing R] [inst_1 : CommRing Rₘ] [inst_2 : CommRing Sₘ]
(M : Submonoid R) [inst_3 : Algebra R Sₘ] [inst_4 : Algebra R Rₘ] [inst_5 : Algebra Rₘ Sₘ] [IsScalarTower R Rₘ Sₘ]
[IsLocalization M Rₘ] [Algebra.FormallySmooth R Sₘ], Algebra.FormallySmooth Rₘ Sₘ- Defined in
- Mathlib.RingTheory.Smooth.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 130 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.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomproof · cited by 10,189
- Idealproof · cited by 4,748
- Bot.botproof · cited by 4,720
- Algebra.algebraMapproof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- AlgHomproof · cited by 3,236
- Submonoidstatement and proof · cited by 3,086
- HasQuotient.Quotientproof · cited by 2,301
- RingHom.compproof · cited by 899
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.FormallyEtale.localization_baseproof · cited by 2
- Algebra.FormallySmooth.localization_mapproof · cited by 0