Theorems · Theorem · commutative algebra
IsLocalizedModule.isTorsionFree_of_forall_isRegular
∀ {R : Type u_1} {M : Type u_2} {A : Type u_3} {N : Type u_4} [inst : CommRing R] [inst_1 : AddCommMonoid M]
[inst_2 : Module R M] [inst_3 : CommRing A] [inst_4 : AddCommMonoid N] [inst_5 : Module A N] [inst_6 : Algebra R A]
[inst_7 : Module R N] [IsScalarTower R A N] (f : M →ₗ[R] N) (S : Submonoid R),
(∀ s ∈ S, s ≠ 0 → IsRegular s) →
∀ [Module.IsTorsionFree R M] [IsLocalization S A] [IsLocalizedModule S f], Module.IsTorsionFree A N- Cited by
- 1 results in Mathlib
- Foundations
- Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- CommRingstatement and proof · cited by 17,173
- AddCommMonoidstatement and proof · cited by 12,281
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement and proof · cited by 10,215
- IsScalarTowerstatement and proof · cited by 3,896
- Submonoidstatement and proof · cited by 3,086
- SMulCommClassproof · cited by 1,927
- zero_smulproof · cited by 716
- IsLocalizationstatement and proof · cited by 636
- Module.IsTorsionFreestatement and proof · cited by 600
Cited by1
Results whose statement or proof uses this declaration.
- IsLocalizedModule.isTorsionFreeproof · cited by 0