Near-rings with \(P\)-central \(P\)-nilpotent or \(P\)-idempotent elements. (English) Zbl 1426.16040
Summary: 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.
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