Theorems · Theorem · commutative algebra
IsLocalization.flat
∀ {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], Module.Flat R S- Defined in
- Mathlib.RingTheory.Flat.Localization
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites37
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Moduleproof · cited by 20,661
- RingHom.idproof · cited by 18,349
- AddCommMonoidproof · cited by 12,281
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Submoduleproof · cited by 7,192
- mul_oneproof · cited by 3,885
- LinearEquivproof · cited by 3,317
- Submonoidstatement and proof · cited by 3,086
- TensorProductproof · cited by 2,545
- LinearMap.compproof · cited by 1,642
Cited by4
Results whose statement or proof uses this declaration.
- RingTheory.Sequence.IsWeaklyRegular.of_isLocalizedModuleproof · cited by 2
- Module.flat_iff_of_isLocalizationproof · cited by 2
- IsSMulRegular.of_isLocalizedModuleproof · cited by 1
- RingHom.Flat.holdsForLocalizationAwayproof · cited by 1