On Higher Derivations and Higher Homomorphisms of Prime Rings

This work consists of three chapters. Chapter one contains fundamental concepts which are basic in our study, we extend N.M.Shammu's theorem to higher N-derivation (by giving the definition of higher N-derivation) and we have answered to the question of Haetinger and Cortes whether the result of Ferro and Haetinger is also true for Jordan generalized triple higher derivation. Chapter two is concerned with higher (U,R) -derivation and generalized higher (U,R) -derivation. We extend and generalized R. Awtar's theorem of derivation of prime ring by giving the concepts of (U,R)-derivation and generalized (U,R)-derivation. Then we extend and generalized this results to higher (U,R)-derivation and generalized (U,R) higher derivation by giving the corresponding definitions. Chapter three concerned with Jordan higher homomorphism and genraralized Jordan higher homomorphism. We extend Bresar's result of Jordan triple homomorphism of prime ring by giving the definitions of (Jordan, Jordan triple) higher homomorphism and we have introduced the definitions of generalized (Jordan, Jordan triple) higher homomorphism to study these concepts onto 2-torsion free prime ring.