Theorems · Theorem · commutative algebra

Derivation.leibniz_pow

∀ {R : Type u_1} {A : Type u_2} {M : Type u_4} [inst : CommSemiring R] [inst_1 : CommSemiring A]
  [inst_2 : AddCommMonoid M] [inst_3 : Algebra R A] [inst_4 : Module A M] [inst_5 : Module R M] (D : Derivation R A M)
  (a : A) (n : ℕ), D (a ^ n) = n • a ^ (n - 1) • D a

Defined in

Mathlib.RingTheory.Derivation.Basic

Cited by

10 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringAddCommMonoidAlgebraModuleModule