Theorems · Definition · commutative algebra

RingHom.quotientKerEquivOfSurjective

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

The first isomorphism theorem for commutative rings, surjective case.

Defined in

Mathlib.RingTheory.Ideal.Quotient.Operations

Cited by

4 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingSemiring