Theorems · Definition · commutative algebra

TensorProduct.Algebra.moduleAux

{R : Type u_1} →
  {A : Type u_2} →
    {B : Type u_3} →
      {M : Type u_4} →
        [inst : CommSemiring R] →
          [inst_1 : AddCommMonoid M] →
            [inst_2 : Module R M] →
              [inst_3 : Semiring A] →
                [inst_4 : Semiring B] →
                  [inst_5 : Module A M] →
                    [inst_6 : Module B M] →
                      [inst_7 : Algebra R A] →
                        [inst_8 : Algebra R B] →
                          [IsScalarTower R A M] → [IsScalarTower R B M] → TensorProduct R A B →ₗ[R] M →ₗ[R] M

An auxiliary definition, used for constructing the Module (A ⊗[R] B) M in TensorProduct.Algebra.module below.

Defined in

Mathlib.RingTheory.TensorProduct.Basic

Cited by

2 results in Mathlib

Foundations

Depth 57 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleSemiringSemiringModuleModuleAlgebraAlgebraIsScalarTowerIsScalarTower