Theorems · Theorem · group theory
eq_zero_of_pow_eq_zero
∀ {R : Type u_3} {x : R} [inst : Zero R] [inst_1 : Pow R ℕ] [IsReduced R] {n : ℕ}, x ^ n = 0 → x = 0- Defined in
- Mathlib.Algebra.GroupWithZero.Basic
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
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.
- IsReducedstatement and proof · cited by 98
- IsReduced.eq_zeroproof · cited by 4
Cited by30
Results whose statement or proof uses this declaration.
- pow_ne_zeroproof · cited by 208
- pow_eq_zero_iffproof · cited by 16
- WeierstrassCurve.Projective.X_eq_zero_of_Z_eq_zeroproof · cited by 12
- Real.cos_pi_div_threeproof · cited by 5
- isLittleO_pow_pow_of_lt_leftproof · cited by 5
- IsCyclotomicExtension.discr_prime_pow_ne_twoproof · cited by 4
- powers_le_nonZeroDivisors_of_noZeroDivisorsproof · cited by 4
- ENNReal.continuous_powproof · cited by 3
- not_isPrimePow_zeroproof · cited by 3
- IsPrimitiveRoot.norm_pow_sub_one_twoproof · cited by 3
- LinearMap.BilinForm.apply_apply_same_eq_zero_iffproof · cited by 3
- NumberField.Embeddings.pow_eq_one_of_norm_le_oneproof · cited by 2