Theorems · Theorem · commutative algebra

Derivation.map_smul_of_tower

∀ {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] {S : Type u_5}
  [inst_6 : SMul S A] [inst_7 : SMul S M] [LinearMap.CompatibleSMul A M S R] (D : Derivation R A M) (r : S) (a : A),
  D (r • a) = r • D a

Defined in

Mathlib.RingTheory.Derivation.Basic

Cited by

2 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringAddCommMonoidAlgebraModuleModuleSMulSMulLinearMap.CompatibleSMul