Theorems · Definition · commutative algebra

RingHom.quotientKerEquivOfRightInverse

{R : Type u} →
  {S : Type v} →
    [inst : Ring R] →
      [inst_1 : Semiring S] → {f : R →+* S} → {g : S → R} → Function.RightInverse g ⇑f → R ⧸ RingHom.ker f ≃+* S

The first isomorphism theorem for commutative rings, computable version.

Defined in

Mathlib.RingTheory.Ideal.Quotient.Operations

Cited by

3 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingSemiring