Theorems · Theorem · ring theory
eq_of_isNilpotent_sub_of_isIdempotentElem_of_commute
∀ {R : Type u_1} [inst : Ring R] {e₁ e₂ : R},
IsIdempotentElem e₁ → IsIdempotentElem e₂ → IsNilpotent (e₁ - e₂) → Commute e₁ e₂ → e₁ = e₂- Defined in
- Mathlib.RingTheory.Idempotents
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Monoidproof · cited by 3,887
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- zero_addproof · cited by 2,366
- MulZeroClass.mul_zeroproof · cited by 2,091
- mul_assocproof · cited by 1,667
- MulZeroClass.zero_mulproof · cited by 1,625
- pow_zeroproof · cited by 1,094
- pow_oneproof · cited by 894
- add_assocproof · cited by 746
- Commutestatement and proof · cited by 639
Cited by2
Results whose statement or proof uses this declaration.
- CompleteOrthogonalIdempotents.of_ker_isNilpotent_of_isMulCentralproof · cited by 1
- eq_of_isNilpotent_sub_of_isIdempotentElemproof · cited by 1