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Module.isTorsionFree_iff_faithfulSMul

∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A] [IsDomain R] [IsDomain A],
  Module.IsTorsionFree R A ↔ FaithfulSMul R A
Defined in
Mathlib.Algebra.Algebra.Basic
Cited by
2 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingRingAlgebraIsDomainIsDomain
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Module.isTorsionFree_iff_algebraMap_injective · cited by 6Module.isTorsionFree_iff_…NoZeroSMulDivisors.iff_faithfulSMul · cited by 0NoZeroSMulDivisors.iff_fa…CommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraRing · cited by 7463RingIsDomain · cited by 2196IsDomainModule.IsTorsionFree · cited by 600Module.IsTorsionFreeFaithfulSMul · cited by 340FaithfulSMulModule.isTorsionFree_iff_fait…CITED BYCITES

Cites6

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Cited by2

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