Theorems · Definition · ring theory

GradedAlgHom.restrictScalars

{R : Type u_1} →
  {A : Type u_6} →
    {B : Type u_7} →
      {ι : Type u_10} →
        [inst : CommSemiring R] →
          [inst_1 : Semiring A] →
            [inst_2 : Semiring B] →
              [inst_3 : Algebra R A] →
                [inst_4 : Algebra R B] →
                  [inst_5 : DecidableEq ι] →
                    [inst_6 : AddMonoid ι] →
                      {𝒜 : ι → Submodule R A} →
                        {ℬ : ι → Submodule R B} →
                          [inst_7 : GradedAlgebra 𝒜] →
                            [inst_8 : GradedAlgebra ℬ] →
                              (R₀ : Type u_11) →
                                [inst_9 : CommSemiring R₀] →
                                  [inst_10 : Algebra R₀ R] →
                                    [inst_11 : Algebra R₀ A] →
                                      [inst_12 : Algebra R₀ B] →
                                        [inst_13 : IsScalarTower R₀ R A] →
                                          [inst_14 : IsScalarTower R₀ R B] →
                                            (𝒜 →ₐᵍ[R] ℬ) →
                                              (fun x => Submodule.restrictScalars R₀ (𝒜 x)) →ₐᵍ[R₀] fun x =>
                                                Submodule.restrictScalars R₀ (ℬ x)

Restrict the base ring to a "smaller" ring.

Defined in

Mathlib.RingTheory.GradedAlgebra.AlgHom

Cited by

6 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringSemiringAlgebraAlgebraDecidableEqAddMonoidGradedAlgebraGradedAlgebraCommSemiringAlgebraAlgebraAlgebraIsScalarTowerIsScalarTower