Theorems · Theorem · ring theory
DirectSum.isIdempotentElem_idempotent
∀ {R : Type u_1} {I : Type u_2} [inst : Semiring R] [inst_1 : DecidableEq I] (V : I → Ideal R)
[inst_2 : DirectSum.Decomposition V] (i : I), IsIdempotentElem (DirectSum.idempotent V i)- Defined in
- Mathlib.Algebra.DirectSum.Idempotents
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Idealstatement and proof · cited by 4,748
- DirectSumproof · cited by 446
- IsIdempotentElemstatement · cited by 217
- DirectSum.decomposeproof · cited by 93
- DirectSum.Decompositionstatement and proof · cited by 57
- DirectSum.decompose_coeproof · cited by 17
- DirectSum.of_eq_sameproof · cited by 12
- DirectSum.idempotentstatement and proof · cited by 3
- DirectSum.decompose_eq_mul_idempotentproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- DirectSum.completeOrthogonalIdempotents_idempotentproof · cited by 0