Theorems · Definition · commutative algebra

Derivation.compAlgebraMap

{R : Type u_1} →
  (A : Type u_2) →
    {B : Type u_3} →
      {M : Type u_4} →
        [inst : CommSemiring R] →
          [inst_1 : CommSemiring A] →
            [inst_2 : CommSemiring B] →
              [inst_3 : AddCommMonoid M] →
                [inst_4 : Algebra R A] →
                  [inst_5 : Algebra R B] →
                    [inst_6 : Module A M] →
                      [inst_7 : Module B M] →
                        [inst_8 : Module R M] →
                          [inst_9 : Algebra A B] →
                            [IsScalarTower R A B] → [IsScalarTower A B M] → Derivation R B M → Derivation R A M

For a tower R → A → B and an R-derivation B → M, we may compose with A → B to obtain an R-derivation A → M.

Defined in

Mathlib.RingTheory.Derivation.Basic

Cited by

4 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringCommSemiringAddCommMonoidAlgebraAlgebraModuleModuleModuleAlgebraIsScalarTowerIsScalarTower