Theorems · Theorem · linear algebra
TensorProduct.quotTensorEquivQuotSMul_mk_tmul
∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (I : Ideal R)
(r : R) (x : M),
(TensorProduct.quotTensorEquivQuotSMul M I) ((Ideal.Quotient.mk I) r ⊗ₜ[R] x) = Submodule.Quotient.mk (r • x)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- RingHomstatement · cited by 10,189
- Top.topstatement · cited by 9,680
- Submodulestatement · cited by 7,192
- Idealstatement and proof · cited by 4,748
- mul_oneproof · cited by 3,885
- LinearEquivstatement · cited by 3,317
- TensorProductstatement · cited by 2,545
Cited by3
Results whose statement or proof uses this declaration.
- TensorProduct.quotTensorEquivQuotSMul_mk_one_tmulproof · cited by 1
- TensorProduct.tensorQuotEquivQuotSMul_tmul_mkproof · cited by 1
- TensorProduct.quotTensorEquivQuotSMul_comp_mkQ_rTensorproof · cited by 1