Theorems · Theorem · commutative algebra
TensorProduct.zero_tmul
∀ {R : Type u_1} [inst : CommSemiring R] (M : Type u_7) {N : Type u_8} [inst_1 : AddCommMonoid M]
[inst_2 : AddCommMonoid N] [inst_3 : Module R M] [inst_4 : Module R N] (n : N), 0 ⊗ₜ[R] n = 0- Defined in
- Mathlib.LinearAlgebra.TensorProduct.Defs
- Cited by
- 40 results in Mathlib
- Foundations
- Depth 42 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- TensorProductstatement · cited by 2,545
- TensorProduct.tmulstatement · cited by 1,182
- FreeAddMonoid.ofproof · cited by 69
- Quotient.sound'proof · cited by 30
Cited by40
Results whose statement or proof uses this declaration.
- TensorProduct.sum_tmulproof · cited by 6
- finsuppTensorFinsupp_applyproof · cited by 5
- TensorProduct.sum_tmul_eq_zero_of_vanishesTriviallyproof · cited by 4
- RingHom.SurjectiveOnStalks.exists_mul_eq_tmulproof · cited by 4
- Algebra.isEpi_iff_forall_one_tmul_eqproof · cited by 3
- KaehlerDifferential.tensorKaehlerEquiv_tmul_Dproof · cited by 3
- Algebra.isEpi_iff_surjective_algebraMap_of_finiteproof · cited by 2
- Matrix.single_kroneckerTMul_singleproof · cited by 2
- PrimeSpectrum.mem_image_comap_zeroLocus_sdiffproof · cited by 2
- TensorProduct.equivFinsuppOfBasisLeft_symmproof · cited by 2
- TensorProduct.ite_tmulproof · cited by 2
- Module.FaithfullyFlat.rTensor_reflects_exactproof · cited by 2