Theorems · Theorem · commutative algebra
IsNilpotent.neg
∀ {R : Type u_1} {x : R} [inst : Ring R], IsNilpotent x → IsNilpotent (-x)- Defined in
- Mathlib.RingTheory.Nilpotent.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- MulZeroClass.mul_zeroproof · cited by 2,091
- IsNilpotentstatement and proof · cited by 248
- neg_powproof · cited by 14
Cited by5
Results whose statement or proof uses this declaration.
- IsNilpotent.exp_neg_mul_exp_selfproof · cited by 1
- IsNilpotent.isUnit_add_oneproof · cited by 1
- IsNilpotent.exp_mul_exp_neg_selfproof · cited by 1
- isNilpotent_neg_iffproof · cited by 1
- not_isNilpotent_neg_oneproof · cited by 1