Theorems · Definition · ring theory
SetLike.GradeZero.subsemiring
{ι : Type u_1} →
{σ : Type u_2} →
{R : Type u_4} →
[inst : Semiring R] →
[inst_1 : AddMonoid ι] →
[inst_2 : SetLike σ R] → [AddSubmonoidClass σ R] → (A : ι → σ) → [SetLike.GradedMonoid A] → Subsemiring RThe subsemiring A 0 of R.
- Defined in
- Mathlib.Algebra.DirectSum.Internal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Submonoidproof · cited by 3,086
- AddMonoidstatement and proof · cited by 2,864
- SetLikestatement and proof · cited by 1,084
- Subsemiringstatement · cited by 456
- AddSubmonoidClassstatement and proof · cited by 346
- SetLike.GradedMonoidstatement and proof · cited by 48
- SetLike.GradeZero.submonoidproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- GradedRing.projZeroRingHom'proof · cited by 4
- SetLike.GradeZero.subringproof · cited by 0
- SetLike.GradeZero.subalgebraproof · cited by 0