Theorems · Theorem · linear algebra

Ideal.map_includeLeft_eq

∀ {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] (I : Ideal A),
  Submodule.restrictScalars R (Ideal.map Algebra.TensorProduct.includeLeft I) =
    (LinearMap.rTensor B (Submodule.restrictScalars R I).subtype).range

The ideal of A ⊗[R] B generated by I is the image of I ⊗[R] B

Defined in

Mathlib.LinearAlgebra.TensorProduct.RightExactness

Cited by

1 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringSemiringAlgebraAlgebra