Theorems · Definition · commutative algebra

Derivation.restrictScalars

(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 : CommSemiring S] →
                      [inst_7 : Algebra S A] →
                        [inst_8 : Module S M] → [LinearMap.CompatibleSMul A M R S] → Derivation S A M → Derivation R A M

If A is both an R-algebra and an S-algebra; M is both an R-module and an S-module, then an S-derivation A → M is also an R-derivation if it is also R-linear.

Defined in

Mathlib.RingTheory.Derivation.Basic

Cited by

4 results in Mathlib

Foundations

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

Assumes

CommSemiringCommSemiringAddCommMonoidAlgebraModuleModuleCommSemiringAlgebraModuleLinearMap.CompatibleSMul