Theorems · Definition · commutative algebra

Subalgebra.LinearDisjoint.mulMapLeftOfSupEqTop

{R : Type u} →
  {S : Type v} →
    [inst : CommSemiring R] →
      [inst_1 : CommSemiring S] →
        [inst_2 : Algebra R S] →
          {A B : Subalgebra R S} → A.LinearDisjoint B → A ⊔ B = ⊤ → TensorProduct R ↥A ↥B ≃ₐ[↥A] S

If A and B are linearly disjoint subalgebras in a commutative algebra S over R such that A ⊔ B = S, then this is the natural isomorphism A ⊗[R] B ≃ₐ[A] S induced by multiplication in S.

Defined in

Mathlib.RingTheory.LinearDisjoint

Cited by

5 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringAlgebra