Theorems · Definition · linear algebra

TensorProduct.AlgebraTensorModule.tensorQuotientEquiv

{R : Type u_1} →
  (A : Type u_2) →
    (B : Type u_3) →
      [inst : CommRing R] →
        [inst_1 : CommRing A] →
          [inst_2 : Algebra R A] →
            [inst_3 : CommRing B] →
              [inst_4 : Algebra R B] →
                (M : Type u_4) →
                  [inst_5 : AddCommGroup M] →
                    [inst_6 : Module R M] →
                      [inst_7 : Module A M] →
                        [inst_8 : IsScalarTower R A M] →
                          {N : Type u_5} →
                            [inst_9 : AddCommGroup N] →
                              [inst_10 : Module R N] →
                                [inst_11 : Module B N] →
                                  [inst_12 : IsScalarTower R B N] →
                                    (n : Submodule B N) →
                                      TensorProduct R M (N ⧸ n) ≃ₗ[A]
                                        TensorProduct R M N ⧸
                                          ((TensorProduct.AlgebraTensorModule.lTensor A M) (↑R n.subtype)).range

More linear version of TensorProduct.tensorQuotientEquiv.

Defined in

Mathlib.LinearAlgebra.TensorProduct.Quotient

Cited by

2 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingAlgebraAddCommGroupModuleModuleIsScalarTowerAddCommGroupModuleModuleIsScalarTower