Theorems · Theorem · group theory
IsReduced.eq_zero
∀ {R : Type u_5} {inst : Zero R} {inst_1 : Pow R ℕ} [self : IsReduced R] (x : R), IsNilpotent x → x = 0A reduced structure has no nonzero nilpotent elements.
- Defined in
- Mathlib.Algebra.GroupWithZero.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- IsReduced
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsNilpotentstatement · cited by 248
- IsReducedstatement and proof · cited by 98
Cited by4
Results whose statement or proof uses this declaration.
- eq_zero_of_pow_eq_zeroproof · cited by 30
- IsNilpotent.eq_zeroproof · cited by 13
- iterateFrobenius_injproof · cited by 4
- minpoly.isRadicalproof · cited by 2