Theorems · Definition · ring theory

AlgEquiv.prodCongr

{R : Type u_1} →
  [inst : CommSemiring R] →
    {S : Type u_5} →
      {T : Type u_6} →
        {A : Type u_7} →
          {B : Type u_8} →
            [inst_1 : Semiring A] →
              [inst_2 : Semiring B] →
                [inst_3 : Semiring S] →
                  [inst_4 : Semiring T] →
                    [inst_5 : Algebra R S] →
                      [inst_6 : Algebra R T] →
                        [inst_7 : Algebra R A] →
                          [inst_8 : Algebra R B] → (S ≃ₐ[R] A) → (T ≃ₐ[R] B) → (S × T) ≃ₐ[R] A × B

Product of algebra isomorphisms.

Defined in

Mathlib.Algebra.Algebra.Prod

Cited by

4 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringSemiringSemiringSemiringAlgebraAlgebraAlgebraAlgebra