Theorems · Definition · commutative algebra

Submodule.toBaseChange.toLinearEquiv

{R : Type u_1} →
  (A : Type u_3) →
    [inst : CommSemiring R] →
      [inst_1 : Semiring A] →
        [inst_2 : Algebra R A] →
          [Module.Flat R A] →
            {M : Type u_5} →
              [inst_4 : AddCommMonoid M] →
                [inst_5 : Module R M] → (p : Submodule R M) → TensorProduct R A ↥p ≃ₗ[A] ↥(Submodule.baseChange A p)

Submodule.toBaseChange as a LinearEquiv.

Defined in

Mathlib.RingTheory.Flat.Basic

Cited by

3 results in Mathlib

Foundations

Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAlgebraModule.FlatAddCommMonoidModule