Theorems · Definition · commutative algebra

HomogeneousIdeal.map

{A : Type u_1} →
  {B : Type u_2} →
    {σ : Type u_4} →
      {τ : Type u_5} →
        {ι : Type u_7} →
          [inst : Semiring A] →
            [inst_1 : Semiring B] →
              [inst_2 : SetLike σ A] →
                [inst_3 : SetLike τ B] →
                  [inst_4 : AddSubmonoidClass σ A] →
                    [inst_5 : AddSubmonoidClass τ B] →
                      [inst_6 : DecidableEq ι] →
                        [inst_7 : AddMonoid ι] →
                          {𝒜 : ι → σ} →
                            {ℬ : ι → τ} →
                              [inst_8 : GradedRing 𝒜] →
                                [inst_9 : GradedRing ℬ] → (𝒜 →+*ᵍ ℬ) → HomogeneousIdeal 𝒜 → HomogeneousIdeal ℬ

Map a homogeneous ideal along a graded ring homomorphism. The underlying ideal is (definitionally) equal to Ideal.map.

Defined in

Mathlib.RingTheory.GradedAlgebra.Homogeneous.Maps

Cited by

30 results in Mathlib

Foundations

Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringSetLikeSetLikeAddSubmonoidClassAddSubmonoidClassDecidableEqAddMonoidGradedRingGradedRing