Theorems · Theorem · group theory
pow_eq_zero_iff
∀ {M₀ : Type u_1} [inst : MonoidWithZero M₀] {a : M₀} {n : ℕ} [IsReduced M₀], n ≠ 0 → (a ^ n = 0 ↔ a = 0)- Defined in
- Mathlib.Algebra.GroupWithZero.Basic
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- MonoidWithZeroIsReduced
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.
- MonoidWithZerostatement and proof · cited by 456
- zero_powproof · cited by 361
- IsReducedstatement and proof · cited by 98
- eq_zero_of_pow_eq_zeroproof · cited by 30
Cited by16
Results whose statement or proof uses this declaration.
- sq_eq_zero_iffproof · cited by 11
- IsCyclotomicExtension.discr_prime_pow_ne_twoproof · cited by 4
- pow_ne_zero_iffproof · cited by 4
- Odd.pow_nonpos_iffproof · cited by 2
- WeierstrassCurve.Jacobian.X_ne_zero_of_Z_eq_zeroproof · cited by 2
- CharTwo.sq_injectiveproof · cited by 2
- IsSepClosed.exists_pow_nat_eqproof · cited by 1
- Field.isAlgebraic_of_adjoin_eq_adjoinproof · cited by 1
- Matrix.isParabolic_iff_of_upperTriangularproof · cited by 1
- Function.support_powproof · cited by 1
- NumberField.mixedEmbedding.norm_eq_zero_iffproof · cited by 0
- Valuation.pow_coeff_zero_ne_zero_of_unitproof · cited by 0