Theorems · Inductive type · group theory
IsMulTorsionFree
(M : Type u_2) → [Monoid M] → Prop
A monoid is torsion-free if power by every non-zero element n : ℕ is injective.
- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 44 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement · cited by 3,887
Cited by48
Results whose statement or proof uses this declaration.
- IsLeftRegular.pow_injectivestatement and proof · cited by 4
- not_isOfFinOrder_of_isMulTorsionFreestatement and proof · cited by 4
- pow_left_injectivestatement and proof · cited by 3
- pow_eq_one_iff_leftstatement and proof · cited by 3
- pow_left_injstatement and proof · cited by 2
- self_eq_invstatement and proof · cited by 2
- MonoidHom.map_negstatement and proof · cited by 2
- not_isMulTorsionFree_of_isMulTorsionstatement · cited by 2
- zpow_left_injstatement and proof · cited by 2
- IsMulTorsionFree.pow_left_injectivestatement and proof · cited by 2
- IsMulTorsionFree.pow_right_injective₀statement and proof · cited by 2
- isMulTorsionFree_iff_not_isOfFinOrderstatement and proof · cited by 2