Let P be an ideal of a near-ring. In this study, we introduce P-nilpotent element of a near-ring with properties. Also, we show that each element which of both P-nilpotent and P-idempotent is only an element of the ideal P. We investigate the relationships between P‑nilpotent, P-regular, P-idempotent and P-center. Finally, we introduce the near-rings in which P-idempotent elements or P‑nilpotent elements are P-central.

near-ring, P-central P-nilpotent, P-central P-idempotent.