Theorems · Theorem · commutative algebra
Module.flat_of_localized_span
∀ (S : Type u_2) [inst : CommSemiring S] (M : Type u_3) [inst_1 : AddCommMonoid M] [inst_2 : Module S M] (s : Set S), Ideal.span s = ⊤ → (∀ (r : ↑s), Module.Flat S (LocalizedModule.Away (↑r) M)) → Module.Flat S M
- Defined in
- Mathlib.RingTheory.Flat.Localization
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Top.topstatement and proof · cited by 9,680
- Set.Elemstatement and proof · cited by 7,166
- Idealstatement · cited by 4,748
- Ideal.spanstatement and proof · cited by 948
- Submonoid.powersstatement and proof · cited by 408
- Module.Flatstatement and proof · cited by 279
- LocalizedModuleproof · cited by 154
- LocalizedModule.mkLinearMapproof · cited by 76
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