Theorems · Definition · ring theory
SetLike.homogeneousSubmonoid
{ι : Type u_1} →
{R : Type u_2} →
{S : Type u_3} →
[inst : SetLike S R] →
[inst_1 : AddMonoid ι] → [inst_2 : Monoid R] → (A : ι → S) → [SetLike.GradedMonoid A] → Submonoid RWhen A is a SetLike.GradedMonoid A, then the homogeneous elements forms a submonoid.
- Defined in
- Mathlib.Algebra.GradedMonoid
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.ofPredproof · cited by 6,101
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement · cited by 3,086
- AddMonoidstatement and proof · cited by 2,864
- SetLikestatement and proof · cited by 1,084
- SetLike.GradedMonoidstatement and proof · cited by 48
- SetLike.IsHomogeneousElemproof · cited by 18
Cited by4
Results whose statement or proof uses this declaration.
- Ideal.IsHomogeneous.iff_existsstatement and proof · cited by 2
- Ideal.IsHomogeneous.iSupproof · cited by 1
- Ideal.IsHomogeneous.mulproof · cited by 0
- Ideal.IsHomogeneous.supproof · cited by 0