Theorems · Definition · commutative algebra

GradedRingHom.gradedAddHom

{ι : Type u_1} →
  {A : Type u_2} →
    {B : Type u_3} →
      {σ : Type u_6} →
        {τ : Type u_7} →
          [inst : Semiring A] →
            [inst_1 : Semiring B] →
              [inst_2 : SetLike σ A] →
                [inst_3 : SetLike τ B] →
                  {𝒜 : ι → σ} →
                    {ℬ : ι → τ} →
                      [inst_4 : AddSubmonoidClass σ A] →
                        [inst_5 : AddSubmonoidClass τ B] → (𝒜 →+*ᵍ ℬ) → (i : ι) → ↥(𝒜 i) →+ ↥(ℬ i)

A graded ring homomorphism descends to an additive homomorphism on each indexed component.

Defined in

Mathlib.RingTheory.GradedAlgebra.RingHom

Cited by

6 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext

Assumes

SemiringSemiringSetLikeSetLikeAddSubmonoidClassAddSubmonoidClass