Theorems · Definition · ring theory
SetLike.IsHomogeneousElem
{ι : Type u_1} → {R : Type u_2} → {S : Type u_3} → [SetLike S R] → (ι → S) → R → PropAn element a : R is said to be homogeneous if there is some i : ι such that a ∈ A i.
- Defined in
- Mathlib.Algebra.GradedMonoid
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- SetLike
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLikestatement and proof · cited by 1,084
Cited by19
Results whose statement or proof uses this declaration.
- SetLike.homogeneousSubmonoidproof · cited by 4
- Ideal.IsHomogeneous.isPrime_of_homogeneous_mem_or_memstatement and proof · cited by 3
- GradedAlgebra.exists_finset_adjoin_eq_top_and_homogeneous_ne_zeroproof · cited by 2
- Ideal.homogeneousCore'_monoproof · cited by 1
- Ideal.homogeneous_spanstatement and proof · cited by 1
- Ideal.mem_homogeneousCore_of_homogeneous_of_memstatement and proof · cited by 1
- GradedAlgebra.exists_finset_adjoin_eq_top_and_homogeneousstatement and proof · cited by 1
- Ideal.IsPrime.homogeneousCoreproof · cited by 1
- SetLike.isHomogeneousElem_coestatement · cited by 1
- Ideal.mul_homogeneous_element_mem_of_memstatement and proof · cited by 1
- Ideal.IsHomogeneous.isPrime_iffstatement and proof · cited by 0
- SetLike.homogeneous_zero_submodulestatement · cited by 0