Theorems · Theorem · ring theory
GradedRing.proj_apply
∀ {ι : Type u_1} {A : Type u_3} {σ : Type u_4} [inst : DecidableEq ι] [inst_1 : AddMonoid ι] [inst_2 : Semiring A]
[inst_3 : SetLike σ A] [inst_4 : AddSubmonoidClass σ A] (𝒜 : ι → σ) [inst_5 : GradedRing 𝒜] (i : ι) (r : A),
(GradedRing.proj 𝒜 i) r = ↑(((DirectSum.decompose 𝒜) r) i)- Defined in
- Mathlib.RingTheory.GradedAlgebra.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Equivstatement · cited by 8,337
- AddMonoidHomstatement · cited by 3,230
- AddMonoidstatement and proof · cited by 2,864
- 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
- DirectSum.decomposestatement · cited by 93
- GradedRing.projstatement · cited by 23
Cited by4
Results whose statement or proof uses this declaration.
- HomogeneousIdeal.mem_irrelevant_of_memproof · cited by 2
- Ideal.mul_homogeneous_element_mem_of_memproof · cited by 1
- AlgebraicGeometry.Proj.iSup_basicOpen_eq_top'proof · cited by 1
- GradedRing.proj_recomposeproof · cited by 0