Theorems · Theorem · commutative algebra
IsAddTorsionFree.of_isTorsionFree
∀ (R : Type u_1) (M : Type u_3) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [Module.IsTorsionFree R M] [IsCancelMulZero R] [CharZero R], IsAddTorsionFree M
- Defined in
- Mathlib.Algebra.Module.Torsion.Free
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- CharZerostatement and proof · cited by 932
- Module.IsTorsionFreestatement and proof · cited by 600
- IsCancelMulZerostatement and proof · cited by 177
- IsAddTorsionFreestatement · cited by 155
- Nat.cast_smul_eq_nsmulproof · cited by 110
- smul_right_injectiveproof · cited by 24
Cited by22
Results whose statement or proof uses this declaration.
- RootPairing.root_sub_root_mem_of_pairingIn_posproof · cited by 7
- RootPairing.setOfPred_root_add_zsmul_eq_Icc_of_linearIndependentproof · cited by 5
- LieAlgebra.IsKilling.exists_isSl2Triple_of_weight_isNonZeroproof · cited by 5
- RootPairing.linearIndependent_of_add_mem_range_root'proof · cited by 3
- RootPairing.extproof · cited by 2
- RootPairing.linearIndependent_iff_coxeterWeight_ne_fourproof · cited by 2
- RootPairing.pairing_one_four_iff'proof · cited by 2
- Ideal.exists_isMaximal_dvd_of_dvd_absNormproof · cited by 2
- RootPairing.GeckConstruction.isNilpotent_eproof · cited by 2
- RootPairing.chainBotCoeff_mul_chainTopCoeff.isNotG2proof · cited by 1
- Ideal.exists_prime_and_absNorm_eq_powproof · cited by 1
- MeasureTheory.integral_eq_zero_of_add_right_eq_negproof · cited by 1