Theorems · Theorem · commutative algebra
isNilpotent_of_pos_nilpotencyClass
∀ {R : Type u_1} {x : R} [inst : Zero R] [inst_1 : Pow R ℕ], 0 < nilpotencyClass x → IsNilpotent x- Defined in
- Mathlib.RingTheory.Nilpotent.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Set.ofPredproof · cited by 6,101
- Set.Nonemptyproof · cited by 2,627
- InfSet.sInfproof · cited by 935
- IsNilpotentstatement · cited by 248
- Set.not_nonempty_iff_eq_emptyproof · cited by 56
- nilpotencyClassstatement and proof · cited by 12
- Nat.sInf_emptyproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- pos_nilpotencyClass_iffproof · cited by 2
- eq_zero_of_nilpotencyClass_eq_oneproof · cited by 1