Ring Nilpotent A nilpotent 𝑧 ∈𝑅 of a ring 𝑅 is an element satisfying 𝑧ℓ =0 for some ℓ ∈ℕ. #m/def/ring It immediately follows that such an element is a zero-divisor. #state/tidy | #lang/en | #SemBr