Theorems · Definition · ring theory

GradedRing.projZeroRingHom

{ι : Type u_1} →
  {A : Type u_3} →
    {σ : Type u_4} →
      [inst : Semiring A] →
        [inst_1 : DecidableEq ι] →
          [inst_2 : AddCommMonoid ι] →
            [inst_3 : PartialOrder ι] →
              [CanonicallyOrderedAdd ι] →
                [inst_5 : SetLike σ A] → [inst_6 : AddSubmonoidClass σ A] → (𝒜 : ι → σ) → [GradedRing 𝒜] → A →+* A

If A is graded by a canonically ordered additive monoid, then the projection map x ↦ x₀ is a ring homomorphism.

Defined in

Mathlib.RingTheory.GradedAlgebra.Basic

Cited by

6 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringDecidableEqAddCommMonoidPartialOrderCanonicallyOrderedAddSetLikeAddSubmonoidClassGradedRing