Theorems · Theorem · commutative algebra
Module.flat_of_localized_maximal
∀ {R : Type u_1} [inst : CommSemiring R] (M : Type u_3) [inst_1 : AddCommMonoid M] [inst_2 : Module R M],
(∀ (P : Ideal R) [inst_3 : P.IsMaximal], Module.Flat R (LocalizedModule P.primeCompl M)) → Module.Flat R M- Defined in
- Mathlib.RingTheory.Flat.Localization
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement and proof · cited by 4,748
- Ideal.primeComplstatement and proof · cited by 462
- Ideal.IsMaximalstatement and proof · cited by 452
- Module.Flatstatement and proof · cited by 279
- LocalizedModulestatement and proof · cited by 154
- LocalizedModule.mkLinearMapproof · cited by 76
- Module.flat_of_isLocalized_maximalproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.