Derivations on prime rings and lie triple systems

In this thesis, some properties from works which have been done up till now aboutJordan derivations of prime and semiprime rings and Lie triple systems are given.This thesis essentially consists of five chapters.In the first chapter, subject of the thesis is introduced and a short information aboutthe works, done so far related to this subject, is given. In the second chapter, thegeneral background and results which may help to make the understanding and thereading of this thesis easier is fixed.In the third chapter , the work of Herstein [13] which is published in 1956is considered essentially and the Jordan homomorphisms of prime rings whosecharacteristics are different from 2 ve 3 are studied.In the first and second section of the fourth chapter, some studies which showthat every derivation in rings is a Jordan derivation but each Jordan derivation inrings is a derivation only under some conditions are studied. In the third sectionof the same chapter, the properties of the ring and conditions for that generalizedJordan derivations in this ring are generalized derivations are given. And inthe fourth section of this chapter, a similar work is obtained for the generalizedJordan triple derivations. Again in the last two sections of the same chapter, theproperties of the Jordan (? ,?)-derivation on a prime ring and generalized Jordantriple (? ,?)-derivations of semiprime rings are mentioned.In the fifth chapter, A. Najati?s 2009 and 2010 papers are studied. Jordan derivationand Jordan triple derivation are defined on the Lie triple systems and in theframework of the fourth chapter, the properties that they satisfy in these systemsare given.