Theorems · Theorem · linear algebra
Module.Basis.isTorsionFree
∀ {ι : Type u_1} {R : Type u_3} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
(b : Module.Basis ι R M), Module.IsTorsionFree R M- Defined in
- Mathlib.LinearAlgebra.Basis.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Module.Basisstatement and proof · cited by 1,477
- Module.IsTorsionFreestatement · cited by 600
- map_smulproof · cited by 566
- Module.Basis.reprproof · cited by 498
- LinearEquiv.injectiveproof · cited by 162
- Function.Injective.moduleIsTorsionFreeproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Module.Basis.algebraMap_injectiveproof · cited by 1
- Module.Basis.smul_eq_zeroproof · cited by 1