Theorems · Definition · ring theory

AddEquiv.toRingEquiv

{R : Type u_7} →
  {S : Type u_8} →
    {F : Type u_9} →
      [inst : Add R] →
        [inst_1 : Add S] →
          [inst_2 : Mul R] →
            [inst_3 : Mul S] →
              [inst_4 : EquivLike F R S] →
                [AddEquivClass F R S] → (f : F) → (∀ (x y : R), f (x * y) = f x * f y) → R ≃+* S

Gives a RingEquiv from an element of an AddEquivClass preserving addition.

Defined in

Mathlib.Algebra.Ring.Equiv

Cited by

0 results in Mathlib

Foundations

Depth 15 from the axioms · uses Quot.sound

Assumes

AddAddMulMulEquivLikeAddEquivClass