Theorems · Theorem · commutative algebra
TensorProduct.tmul_zero
∀ {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] (m : M), m ⊗ₜ[R] 0 = 0- Defined in
- Mathlib.LinearAlgebra.TensorProduct.Defs
- Cited by
- 44 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 by44
Results whose statement or proof uses this declaration.
- TensorProduct.tmul_sumproof · cited by 10
- finsuppTensorFinsupp_applyproof · cited by 5
- Ideal.comap_map_eq_self_of_faithfullyFlatproof · cited by 4
- Algebra.Generators.H1Cotangent.δAux_monomialproof · cited by 3
- TensorProduct.finsuppRight_apply_tmul_applyproof · cited by 3
- TensorProduct.finsuppRight_tmul_singleproof · cited by 3
- Matrix.single_kroneckerTMul_singleproof · cited by 2
- TensorProduct.directSumRight_tmulproof · cited by 2
- TensorProduct.tmul_iteproof · cited by 2
- Algebra.Generators.H1Cotangent.δAux_Xproof · cited by 2
- TensorProduct.exists_finsupp_leftproof · cited by 2
- Algebra.Extension.Cotangent.mk_C_mem_ker_cotangentComplexproof · cited by 2