Prime ideals and radicals of the near-rings and smarandache near-rings

The purpose of this thesis is to study the concept of near-rings, Smarandache near-rings, examining some related features and researching some theorems and results. In addition, because of the near-rings, generalized version of the rings, studies and researches in this field are carried out regularly and continuously. Historically, the first studies on the near-ring were done by L.E. dıckson in 1905. Vasantha Kandasamy did his first work on Smarandache near-rings in 2002. Different results have been obtained by extending many concepts in rings in near-rings. In this study, it has been shown that it can create different near-ring structures on each G group. In addition, it has been investigated that in the N near-ring the annihilator of each element is a left ideal requirement and generally there is no sub near-ring. Then the concepts of S-near-ring, S-sub near-ring and S-near-ring homomorphism are explained by giving examples. Finally, examples are presented with prime, semi-prime ideals and related theorems on the prime radical of an ideal. Key Words: Near-ring, N-group,Near-ring Homomorphism,Group Near-ring, S-near- ring, S-ideal, Prime Ideal, Semi Prime Ideal, Prime Radical.