Theorems · Inductive type · ring theory
OrthogonalIdempotents
{R : Type u_1} → [Semiring R] → {I : Type u_3} → (I → R) → PropA family { eᵢ } of idempotent elements is orthogonal if eᵢ * eⱼ = 0 for all i ≠ j.
- Defined in
- Mathlib.RingTheory.Idempotents
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- Semiring
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.
- Semiringstatement · cited by 13,802
Cited by30
Results whose statement or proof uses this declaration.
- OrthogonalIdempotents.mul_eqstatement and proof · cited by 8
- OrthogonalIdempotents.idemstatement and proof · cited by 7
- CompleteOrthogonalIdempotents.toOrthogonalIdempotentsstatement · cited by 7
- OrthogonalIdempotents.orthostatement and proof · cited by 5
- OrthogonalIdempotents.embeddingstatement and proof · cited by 3
- OrthogonalIdempotents.isIdempotentElem_sumstatement and proof · cited by 2
- OrthogonalIdempotents.optionstatement and proof · cited by 2
- OrthogonalIdempotents.prod_one_substatement and proof · cited by 2
- completeOrthogonalIdempotents_iffstatement and proof · cited by 2
- CompleteOrthogonalIdempotents.equivproof · cited by 2
- CompleteOrthogonalIdempotents.mapproof · cited by 2
- CompleteOrthogonalIdempotents.of_prod_one_substatement and proof · cited by 1