P-regularity and P-v-primeness in near-rings

This thesis consists of four chapters. The literature and basic informations about the study have been given in the first and second chapters. In the third chapter, concepts of P-regularity, P-strongly regularity and P-primeness in near-rings have been investigated in details. Also relationships which being with other concepts in near-rings and with each other of these concepts have been researched. In the fourth chapter, concepts of a P-center of near-ring, P-center of an element and P-right (left) identity by using a given ideal P have been defined. It has been proved that the set of all P-identities in a near-ring is a multiplicative subsemigroup of it has been proved. Also concepts of P-right (left) permutable, P-medial and P-completely prime near-ring have been defined, and some properties and results have been obtained for these near-rings. Furthermore relationships between this concepts and P-regularity, P-strongly regularity and P-idempotent elements have been examined.