Characterizations of Prime and Semiprime Gamma Rings with Derivations

Gamma ring was first introduced by N. Nobusawa as a generalization of a classical ring. W. E. Barnes generalized the definition of a gamma ring due to Nobusawa. Presently the gamma ring due to Barnes is known as a gamma ring and gamma ring due to Nobusawa is known as gamma ring in the sense of Nobusawa and is denoted by Γₙ-ring. It is clear that every ring is a gamma ring and every Γₙ-ring is also a Γ-ring. Actually W.E.Barnes J.Luh and S.Kyuno studied the structures of Γ-rings and obtained various generalizations analogous to the corresponding parts in ring theory. Afterwards a number of algebraists have determined a lot of fundamental properties of Γ-rings to classify and extend numerous significant results in classical ring theory to Γ-ring theory. This work entitled Characterizations of Prime and Semiprime Gamma Rings with Derivations and Lie Ideals aims to characterize prime and semiprime Γ-rings with various types of left derivations derivations generalized derivations higher derivations derivations on Lie ideals and (UM)-derivations.