Theorems · Theorem · commutative algebra

Ideal.quotientKerAlgEquivOfSurjective_apply

∀ {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} (hf : Function.Surjective ⇑f)
  (a : A ⧸ RingHom.ker f.toRingHom), (Ideal.quotientKerAlgEquivOfSurjective hf) a = (↑f).kerLift a

Defined in

Mathlib.RingTheory.Ideal.Quotient.Operations

Cited by

2 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringRingAlgebraSemiringAlgebra