Theorems · Definition · commutative algebra

IsBaseChange

{R : Type u_1} →
  {M : Type v₁} →
    {N : Type v₂} →
      (S : Type v₃) →
        [inst : AddCommMonoid M] →
          [inst_1 : AddCommMonoid N] →
            [inst_2 : CommSemiring R] →
              [inst_3 : CommSemiring S] →
                [inst_4 : Algebra R S] →
                  [inst_5 : Module R M] →
                    [inst_6 : Module R N] → [inst_7 : Module S N] → [IsScalarTower R S N] → (M →ₗ[R] N) → Prop

Given an R-algebra S and an R-module M, an S-module N together with a map f : M →ₗ[R] N is the base change of M to S if the map S × M → N, (s, m) ↦ s • f m is the tensor product.

Defined in

Mathlib.RingTheory.IsTensorProduct

Cited by

87 results in Mathlib

Foundations

Depth 58 from the axioms · uses propext, Quot.sound

Assumes

AddCommMonoidAddCommMonoidCommSemiringCommSemiringAlgebraModuleModuleModuleIsScalarTower