Different prime N-ideals and IFP N-Ideals

We provide some characterizations of completely prime (completely semiprime) and 3-prime (3-semiprime) N -groups. The relationship between a 3-prime (completely prime) N -ideal P of an N -group Γ and the ideal ( P : Γ) of the near-ring N is investigated. Moreover, the notion of IFP N -ideal is defined. We prove that the concept of IFP N -ideal occurs naturally where N is a left permutable (left self distributive, subcommutative) near-ring and Γ a monogenic N -group. Also, we obtain some relationships between an IFP N -ideal P of an N -group Γ and the ideal ( P : Γ) of the near-ring N .