Theorems · Theorem · commutative algebra
LinearMap.rTensor_zero
∀ {R : Type u_1} [inst : CommSemiring R] (M : Type u_7) {N : Type u_8} {P : Type u_9} [inst_1 : AddCommMonoid M]
[inst_2 : AddCommMonoid N] [inst_3 : AddCommMonoid P] [inst_4 : Module R M] [inst_5 : Module R N]
[inst_6 : Module R P], LinearMap.rTensor M 0 = 0- Defined in
- Mathlib.LinearAlgebra.TensorProduct.Map
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 64 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
- RingHom.idstatement · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- TensorProductstatement · cited by 2,545
- LinearMap.rTensorstatement · cited by 266
- LinearMap.map_zeroproof · cited by 52
- LinearMap.rTensorHomproof · cited by 8
Cited by5
Results whose statement or proof uses this declaration.
- lTensor_injective_of_exact_of_exact_of_rTensor_injectiveproof · cited by 2
- Module.Flat.iff_rTensor_exact'proof · cited by 1
- ContinuousLinearMap.rTensor_zeroproof · cited by 1
- Representation.IntertwiningMap.rTensor_zeroproof · cited by 0
- Module.FaithfullyFlat.iff_exact_iff_rTensor_exactproof · cited by 0