Theorems · Theorem · commutative algebra
Module.Flat.of_isLocalizedModule
∀ {R : Type u} {M : Type u_1} {Mp : Type u_2} (Rp : Type v) [inst : CommSemiring R] [inst_1 : AddCommMonoid M]
[inst_2 : Module R M] [inst_3 : CommSemiring Rp] [inst_4 : Algebra R Rp] [inst_5 : AddCommMonoid Mp]
[inst_6 : Module R Mp] [inst_7 : Module Rp Mp] [IsScalarTower R Rp Mp] [Module.Flat R M] (S : Submonoid R)
[IsLocalization S Rp] (f : M →ₗ[R] Mp) [h : IsLocalizedModule S f], Module.Flat Rp Mp- Defined in
- Mathlib.RingTheory.Flat.Stability
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- RingHom.idstatement and proof · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement and proof · cited by 10,215
- IsScalarTowerstatement and proof · cited by 3,896
- Submonoidstatement and proof · cited by 3,086
- IsLocalizationstatement and proof · cited by 636
- Module.Flatstatement and proof · cited by 279
- IsLocalizedModulestatement and proof · cited by 220
- isLocalizedModule_iff_isBaseChangeproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Module.flat_iff_of_isLocalizationproof · cited by 2