Theorems · Definition · ring theory

GradedTensorProduct.tmul

(R : Type u_1) →
  {ι : Type u_2} →
    {A : Type u_3} →
      {B : Type u_4} →
        [inst : CommSemiring ι] →
          [inst_1 : DecidableEq ι] →
            [inst_2 : CommRing R] →
              [inst_3 : Ring A] →
                [inst_4 : Ring B] →
                  [inst_5 : Algebra R A] →
                    [inst_6 : Algebra R B] →
                      {𝒜 : ι → Submodule R A} →
                        {ℬ : ι → Submodule R B} →
                          [inst_7 : GradedAlgebra 𝒜] → [inst_8 : GradedAlgebra ℬ] → A → B → GradedTensorProduct R 𝒜 ℬ

The graded tensor product of two elements of graded rings.

Defined in

Mathlib.LinearAlgebra.TensorProduct.Graded.Internal

Cited by

21 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringDecidableEqCommRingRingRingAlgebraAlgebraGradedAlgebraGradedAlgebra