Theorems · Definition · commutative algebra

Subalgebra.LinearDisjoint.basisOfBasisRight

{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 = ⊤ → {ι : Type u_1} → Module.Basis ι R ↥B → Module.Basis ι (↥A) S

If A and B are linearly disjoint subalgebras in a commutative algebra S over R such that A ⊔ B = S, then any R-basis of B is also an A-basis of S.

Defined in

Mathlib.RingTheory.LinearDisjoint

Cited by

6 results in Mathlib

Foundations

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

Assumes

CommSemiringCommSemiringAlgebra