Theorems · Theorem · ring theory
GradedRing.projZeroRingHom_apply
∀ {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] [inst_4 : CanonicallyOrderedAdd ι] [inst_5 : SetLike σ A] [inst_6 : AddSubmonoidClass σ A]
(𝒜 : ι → σ) [inst_7 : GradedRing 𝒜] (a : A), (GradedRing.projZeroRingHom 𝒜) a = ↑(((DirectSum.decompose 𝒜) a) 0)- Defined in
- Mathlib.RingTheory.GradedAlgebra.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- RingHomstatement · cited by 10,189
- Equivstatement · cited by 8,337
- PartialOrderstatement and proof · cited by 6,410
- SetLikestatement and proof · cited by 1,084
- DFinsuppstatement · cited by 694
- DirectSumstatement · cited by 446
- GradedRingstatement and proof · cited by 424
- AddSubmonoidClassstatement and proof · cited by 346
- CanonicallyOrderedAddstatement and proof · cited by 229
Cited by3
Results whose statement or proof uses this declaration.
- HomogeneousIdeal.irrelevant_eq_iSupproof · cited by 2
- GradedRing.projZeroRingHom'_apply_coeproof · cited by 1
- AlgebraicGeometry.Proj.iSup_basicOpen_eq_top'proof · cited by 1