Theorems · Definition · commutative algebra

AlgHom.kerSquareLift

{R : Type u} →
  [inst : CommRing R] →
    {A : Type u_1} →
      {B : Type u_2} →
        [inst_1 : CommRing A] →
          [inst_2 : CommRing B] →
            [inst_3 : Algebra R A] → [inst_4 : Algebra R B] → (f : A →ₐ[R] B) → A ⧸ RingHom.ker f.toRingHom ^ 2 →ₐ[R] B

The lift of f : A →ₐ[R] B to A ⧸ J ^ 2 →ₐ[R] B with J being the kernel of f.

Defined in

Mathlib.RingTheory.Ideal.Cotangent

Cited by

10 results in Mathlib

Foundations

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

Assumes

CommRingCommRingCommRingAlgebraAlgebra