Mathlib Map

Theorems · Definition · ring theory

GradedRing.proj

{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) → [GradedRing 𝒜] → ι → A →+ A

The projection maps of a graded ring

Defined in
Mathlib.RingTheory.GradedAlgebra.Basic
Cited by
23 results in Mathlib
Foundations
Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidableEqAddMonoidSemiringSetLikeAddSubmonoidClassGradedRing

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier · cited by 9FromSpec.carrierGradedRing.proj_apply · cited by 4GradedRing.proj_applyIdeal.IsHomogeneous.isPrime_of_homogeneous_mem_or_mem · cited by 3IsHomogeneous.isPrime_of_…AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.denom_notMem · cited by 2carrier.denom_notMemAlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.zero_mem · cited by 2carrier.zero_memHomogeneousIdeal.mem_irrelevant_iff · cited by 2HomogeneousIdeal.mem_irre…AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.mem_carrier_iff_of_mem · cited by 2FromSpec.mem_carrier_iff_…AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.add_mem · cited by 1carrier.add_memIdeal.toIdeal_homogeneousHull_eq_iSup · cited by 1Ideal.toIdeal_homogeneous…ProjectiveSpectrum.basicOpen_eq_union_of_projection · cited by 1ProjectiveSpectrum.basicO…AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.asIdeal.homogeneous · cited by 1asIdeal.homogeneousIdeal.mul_homogeneous_element_mem_of_mem · cited by 1Ideal.mul_homogeneous_ele…AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.mem_carrier_iff · cited by 1FromSpec.mem_carrier_iffIdeal.homogeneousHull_eq_iSup · cited by 0Ideal.homogeneousHull_eq_…Subsemiring.isHomogeneous_iff_forall_subset · cited by 0Subsemiring.isHomogeneous…Semiring · cited by 13802SemiringAddMonoidHom · cited by 3230AddMonoidHomAddMonoid · cited by 2864AddMonoidSetLike · cited by 1084SetLikeGradedRing · cited by 424GradedRingAddSubmonoidClass · cited by 346AddSubmonoidClassAddMonoidHom.comp · cited by 339AddMonoidHom.compRingEquiv.toRingHom · cited by 150RingEquiv.toRingHomRingHom.toAddMonoidHom · cited by 17RingHom.toAddMonoidHomAddSubmonoidClass.subtype · cited by 12AddSubmonoidClass.subtypeDirectSum.decomposeRingEquiv · cited by 8DirectSum.decomposeRingEq…DFinsupp.evalAddMonoidHom · cited by 7DFinsupp.evalAddMonoidHomGradedRing.projCITED BYCITES

Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by24

Results whose statement or proof uses this declaration.