Theorems · Definition · ring theory

AddMonoidAlgebra.tensorEquiv

(R : Type u_1) →
  {M : Type u_2} →
    {N : Type u_3} →
      [inst : CommSemiring R] →
        TensorProduct R (AddMonoidAlgebra R M) (AddMonoidAlgebra R N) ≃ₗ[R] AddMonoidAlgebra R (M × N)

The tensor product of two monoid algebras is the monoid algebra of their product.

Defined in: Mathlib.RingTheory.TensorProduct.MonoidAlgebra
Cited by: 4 results in Mathlib
Foundations: Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommSemiring

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Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

RingHom.idstatement · cited by 18,349
CommSemiringstatement and proof · cited by 10,911
LinearEquivstatement · cited by 3,317
TensorProductstatement · cited by 2,545
LinearEquiv.symmproof · cited by 1,461
AddMonoidAlgebrastatement · cited by 649
LinearEquiv.transproof · cited by 298
TensorProduct.congrproof · cited by 50
finsuppTensorFinsupp'proof · cited by 24
AddMonoidAlgebra.coeffLinearEquivproof · cited by 15

Cited by4

Results whose statement or proof uses this declaration.

AddMonoidAlgebra.coeff_tensorEquiv_applystatement and proof · cited by 1
AddMonoidAlgebra.tensorEquiv_single_tmul_singlestatement · cited by 0
AddMonoidAlgebra.tensorEquiv_symm_single_eq_single_zero_tmulstatement · cited by 0
AddMonoidAlgebra.tensorEquiv_symm_single_eq_tmul_single_zerostatement · cited by 0