Theorems · Theorem · ring theory
CompleteOrthogonalIdempotents.of_ker_isNilpotent
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : Ring S] (f : R →+* S) {I : Type u_3} [inst_2 : Fintype I]
{e : I → R},
(∀ x ∈ RingHom.ker f, IsNilpotent x) →
(∀ (i : I), IsIdempotentElem (e i)) → CompleteOrthogonalIdempotents (⇑f ∘ e) → CompleteOrthogonalIdempotents e- Defined in
- Mathlib.RingTheory.Idempotents
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- Fintypestatement and proof · cited by 7,736
- Ringstatement and proof · cited by 7,463
- Idealstatement · cited by 4,748
- mul_commproof · cited by 2,262
- RingHom.kerstatement and proof · cited by 363
- IsNilpotentstatement and proof · cited by 248
- IsIdempotentElemstatement and proof · cited by 217
- CompleteOrthogonalIdempotentsstatement and proof · cited by 27
- Semigroup.mem_center_iffproof · cited by 12
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