Theorems · Theorem · commutative algebra
IsIdempotentElem.eq_zero_of_isNilpotent
∀ {R : Type u_1} [inst : MonoidWithZero R] {e : R}, IsIdempotentElem e → IsNilpotent e → e = 0- Defined in
- Mathlib.RingTheory.Nilpotent.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- MonoidWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- one_mulproof · cited by 2,841
- MulZeroClass.zero_mulproof · cited by 1,625
- pow_zeroproof · cited by 1,094
- MonoidWithZerostatement and proof · cited by 456
- IsNilpotentstatement and proof · cited by 248
- IsIdempotentElemstatement and proof · cited by 217
- IsIdempotentElem.pow_succ_eqproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- IsNilpotent.eq_zero_of_isIdempotentElemproof · cited by 0