Theorems · Theorem · commutative algebra
Module.Flat.flat_iff_torsion_eq_bot_of_isBezout
∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [IsBezout R]
[IsDomain R], Module.Flat R M ↔ Submodule.torsion R M = ⊥If R is Bezout then an R-module is flat iff it has no torsion.
- Defined in
- Mathlib.RingTheory.Flat.TorsionFree
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites46
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idproof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapproof · cited by 10,215
- Submodulestatement · cited by 7,192
- Idealproof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- TensorProductproof · cited by 2,545
- IsDomainstatement and proof · cited by 2,196
- LinearMap.compproof · cited by 1,642
Cited by1
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