Theorems · Theorem · commutative algebra
DirectSum.subtype_rTensor_injective
∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
(ℳ : ι → Submodule R M) (N : Type u_5) [inst_3 : AddCommMonoid N] [inst_4 : Module R N] [inst_5 : DecidableEq ι]
[DirectSum.Decomposition ℳ] (i : ι), Function.Injective ⇑(LinearMap.rTensor N (ℳ i).subtype)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · 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
- LinearMapstatement · cited by 10,215
- Submodulestatement and proof · cited by 7,192
- TensorProductstatement · cited by 2,545
- LinearMap.compproof · cited by 1,642
- TensorProduct.tmulproof · cited by 1,182
- LinearEquiv.toLinearMapproof · cited by 1,171
- LinearMap.extproof · cited by 844
Cited by1
Results whose statement or proof uses this declaration.
- DirectSum.decomposeTensorEquivproof · cited by 4