D-strong and almostD-strong near-rings

In this paper,D-strong and almostD-strong near-rings have been defined. It has been proved that ifR is aD-strongS-near ring, then prime ideals, strictly prime ideals and completely prime ideals coincide. Also ifR is aD-strong near-ring with identity, then every maximal right ideal becomes a maximal ideal and moreover every 2-primitive near-ring becomes a near-field. Several properties, chain conditions and structure theorems have also been discussed.Most of the parts of this paper are included in author's doctoral dissertation at Sukhadia University Udaipur (1983). The author expresses his gratitude to Dr.S. C. Choudhary for his kind guidance.