Theorems · Definition · linear algebra
TensorProduct.rid
(R : Type u_1) →
[inst : CommSemiring R] →
(M : Type u_5) → [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → TensorProduct R M R ≃ₗ[R] MThe base ring is a right identity for the tensor product of modules, up to linear equivalence.
- Cited by
- 63 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- RingHom.idstatement · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearEquivstatement · cited by 3,317
- TensorProductstatement · cited by 2,545
- LinearMap.flipproof · cited by 193
- TensorProduct.mkproof · cited by 129
- TensorProduct.liftproof · cited by 59
- LinearMap.lsmulproof · cited by 50
- LinearEquiv.ofLinearMapproof · cited by 9
Cited by70
Results whose statement or proof uses this declaration.
- TensorProduct.ridIsometryproof · cited by 9
- Representation.TensorProduct.ridproof · cited by 7
- Algebra.TensorProduct.includeLeft_injectiveproof · cited by 5
- QuadraticForm.tensorRIdproof · cited by 5
- finsuppTensorFinsuppRidproof · cited by 4
- Module.Invertible.rightCancelEquivproof · cited by 4
- Algebra.TensorProduct.basisAuxproof · cited by 3
- SemimoduleCat.MonoidalCategory.rightUnitorproof · cited by 3
- TensorProduct.rid_symm_applystatement · cited by 3
- TensorProduct.rid_tmulstatement · cited by 3
- Algebra.TensorProduct.basisAux_tmulproof · cited by 2
- Algebra.TensorProduct.basis_repr_symm_applyproof · cited by 2