Theorems · Definition · commutative algebra

Ideal.kerLiftAlg

{R₁ : Type u_1} →
  {A : Type u_3} →
    {B : Type u_4} →
      [inst : CommSemiring R₁] →
        [inst_1 : Ring A] →
          [inst_2 : Algebra R₁ A] →
            [inst_3 : Semiring B] → [inst_4 : Algebra R₁ B] → (f : A →ₐ[R₁] B) → A ⧸ RingHom.ker f →ₐ[R₁] B

The induced algebras morphism from the quotient by the kernel to the codomain. This is an isomorphism if f has a right inverse (quotientKerAlgEquivOfRightInverse) / is surjective (quotientKerAlgEquivOfSurjective).

Defined in

Mathlib.RingTheory.Ideal.Quotient.Operations

Cited by

4 results in Mathlib

Foundations

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

Assumes

CommSemiringRingAlgebraSemiringAlgebra