Theorems · Theorem · commutative algebra
Module.flat_iff_of_isLocalization
∀ {R : Type u_1} (S : Type u_2) [inst : CommSemiring R] [inst_1 : CommSemiring S] [inst_2 : Algebra R S]
(p : Submonoid R) [IsLocalization p S] (M : Type u_3) [inst_4 : AddCommMonoid M] [inst_5 : Module R M]
[inst_6 : Module S M] [IsScalarTower R S M], Module.Flat S M ↔ Module.Flat R M- Defined in
- Mathlib.RingTheory.Flat.Localization
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- IsScalarTowerstatement and proof · cited by 3,896
- Submonoidstatement and proof · cited by 3,086
- IsLocalizationstatement and proof · cited by 636
- LinearMap.idproof · cited by 625
- Module.Flatstatement and proof · cited by 279
- IsLocalizedModuleproof · cited by 220
- Module.Flat.transproof · cited by 9
- IsLocalization.flatproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- RingHom.Flat.localRingHomproof · cited by 1