Theorems · Definition · ring theory

AlgEquiv.toAddEquiv

{R : Type u} →
  {A : Type v} →
    {B : Type w} →
      [inst : CommSemiring R] →
        [inst_1 : Semiring A] →
          [inst_2 : Semiring B] → [inst_3 : Algebra R A] → [inst_4 : Algebra R B] → (A ≃ₐ[R] B) → A ≃+ B

Defined in: Mathlib.Algebra.Algebra.Equiv
Cited by: 2 results in Mathlib
Foundations: Depth 13 from the axioms · uses no axioms
Assumes: CommSemiring Semiring Semiring Algebra Algebra

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Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Semiringstatement and proof · cited by 13,802
Algebrastatement and proof · cited by 11,388
CommSemiringstatement and proof · cited by 10,911
AlgEquivstatement and proof · cited by 1,681
AddEquivstatement · cited by 1,087
AlgEquiv.toEquivproof · cited by 65
AlgEquiv.map_add'proof · cited by 19

Cited by3

Results whose statement or proof uses this declaration.

AlgEquiv.toLinearEquivproof · cited by 117
Algebra.IsPushout.symmproof · cited by 7
Algebra.IsEffective.of_isEffective_tensorProduct_of_faithfullyFlatproof · cited by 1