Theorems · Theorem · commutative algebra

liftOfDerivationToSquareZero_mk_apply

∀ {R : Type u} {A : Type v} {B : Type w} [inst : CommSemiring R] [inst_1 : CommSemiring A] [inst_2 : CommRing B]
  [inst_3 : Algebra R A] [inst_4 : Algebra R B] (I : Ideal B) [inst_5 : Algebra A B] (hI : I ^ 2 = ⊥)
  [inst_6 : IsScalarTower R A B] (d : Derivation R A ↥I) (x : A),
  (Ideal.Quotient.mk I) ((liftOfDerivationToSquareZero I hI d) x) = (algebraMap A (B ⧸ I)) x

Defined in

Mathlib.RingTheory.Derivation.ToSquareZero

Cited by

0 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringCommRingAlgebraAlgebraAlgebraIsScalarTower