Theorems · Theorem · linear algebra

TensorProduct.AlgebraTensorModule.range_lTensor_idealMap

∀ {R : Type u_1} [inst : CommSemiring R] (A : Type u_2) {B : Type u_3} [inst_1 : Semiring A] [inst_2 : Semiring B]
  [inst_3 : Algebra R A] [inst_4 : Algebra R B] (S : Type u_4) [inst_5 : CommSemiring S] [inst_6 : Algebra R S]
  [inst_7 : Algebra S A] [inst_8 : IsScalarTower R S A] (I : Ideal B),
  ((TensorProduct.AlgebraTensorModule.lTensor S A) (↑R (Submodule.subtype I))).range =
    Submodule.restrictScalars S (Ideal.map Algebra.TensorProduct.includeRight I)

Defined in

Mathlib.LinearAlgebra.TensorProduct.RightExactness

Cited by

0 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringSemiringAlgebraAlgebraCommSemiringAlgebraAlgebraIsScalarTower