Theorems · Definition · ring theory

GradedTensorProduct

(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) → [GradedAlgebra 𝒜] → [GradedAlgebra ℬ] → Type (max u_4 u_3)

A Type synonym for A ⊗[R] B, but with multiplication as TensorProduct.gradedMul. This has notation 𝒜 ᵍ⊗[R] ℬ.

Defined in

Mathlib.LinearAlgebra.TensorProduct.Graded.Internal

Cited by

37 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringDecidableEqCommRingRingRingAlgebraAlgebraGradedAlgebraGradedAlgebra