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Theorems · Theorem · group theory

Function.Injective.isAddTorsionFree

∀ {M : Type u_4} {N : Type u_5} [inst : AddMonoid M] [inst_1 : AddMonoid N] [IsAddTorsionFree N] (f : M →+ N),
  Function.Injective ⇑f → IsAddTorsionFree M

If the codomain of an injective additive monoid homomorphism is torsion free, then so is the domain.

Defined in
Mathlib.Algebra.Group.Hom.Defs
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Foundations
Depth 12 from the axioms · uses no axioms
Assumes
AddMonoidAddMonoidIsAddTorsionFree
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DFunLike.coe · cited by 62936DFunLike.coeAddMonoidHom · cited by 3230AddMonoidHomAddMonoid · cited by 2864AddMonoidIsAddTorsionFree · cited by 155IsAddTorsionFreemap_nsmul · cited by 41map_nsmulIsAddTorsionFree.nsmul_right_injective · cited by 2IsAddTorsionFree.nsmul_ri…Injective.isAddTorsionFreeCITED BYCITES

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