R S : Type u
x y : R
inst✝ : MonoidWithZero R
⊢ IsRadical 0 ↔ ∀ (x : R) (x_1 : ℕ), 0 ∣ x ^ x_1 → 0 ∣ x
R S : Type u
x y : R
inst✝ : MonoidWithZero R
⊢ IsRadical 0 ↔ IsReduced R
simp_rw [isReduced_iff, IsNilpotent, exists_imp, ← zero_dvd_iff]
no goals
R S : Type u
x y : R
inst✝ : MonoidWithZero R
⊢ IsRadical 0 ↔ ∀ (x : R) (x_1 : ℕ), 0 ∣ x ^ x_1 → 0 ∣ x
exact forall_swap