Theorems · Theorem · commutative algebra
smul_right_inj
∀ {R : Type u_1} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {r : R} {m₁ m₂ : M}
[Module.IsTorsionFree R M] [IsCancelMulZero R], r ≠ 0 → (r • m₁ = r • m₂ ↔ m₁ = m₂)- Defined in
- Mathlib.Algebra.Module.Torsion.Free
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Module.IsTorsionFreestatement and proof · cited by 600
- IsCancelMulZerostatement and proof · cited by 177
- IsRegular.of_ne_zeroproof · cited by 15
- IsRegular.smul_right_injproof · cited by 2
Cited by9
Results whose statement or proof uses this declaration.
- meromorphicOrderAt_eq_int_iffproof · cited by 31
- linearIndepOn_isGroupLikeElemproof · cited by 3
- Polynomial.IsPrimitive.mul_map_mem_lifts_iffproof · cited by 2
- Polynomial.bernoulli_comp_one_add_Xproof · cited by 2
- AnalyticAt.unique_eventuallyEq_zpow_smul_nonzeroproof · cited by 2
- MvPowerSeries.pderiv.extproof · cited by 1
- ZMod.dft_odd_iffproof · cited by 1
- PowerSeries.exp_unique_of_derivative_eq_selfproof · cited by 0
- ZMod.dft_even_iffproof · cited by 0