Theorems · Definition · commutative algebra

IsLocalization.algebraLid

{R : Type u_1} →
  [inst : CommSemiring R] →
    (S : Submonoid R) →
      (A : Type u_2) →
        [inst_1 : CommSemiring A] →
          [inst_2 : Algebra R A] →
            [IsLocalization S A] →
              (B : Type u_5) →
                [inst_4 : Semiring B] →
                  [inst_5 : Algebra R B] → [inst_6 : Algebra A B] → [IsScalarTower R A B] → TensorProduct R A B ≃ₐ[A] B

If A is a localization of R, tensoring an A-algebra with A over R does nothing.

Defined in

Mathlib.RingTheory.Localization.BaseChange

Cited by

0 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraIsLocalizationSemiringAlgebraAlgebraIsScalarTower