On certain maps acting as (anti-)homomorphism in prime rings

This thesis meanly consists of six chapters. In the first chapter, the subject of the thesis is introduced and short information is given about the works that have been done so far related to this subject. In the second chapter, some basic theorems, definitions and properties which may help to make easy understanding and reading of this thesis are given. Furthermore, the types of derivations in rings have been introduced a summary of some works have been done over rings so far and frequently used important results from the references took place in this chapter. In the third chapter, firstly A. Asma, N. Rehman and A. Shakir' s work in 2003 after N. Rehman' s work in 2004 and finally in order to complete some deficiency on N. Rehman' s work in 2004, I. Gusic' s work in 2005 is studied. In the fourth chapter, Ashraf et al.' s work in 2012 is primarily considered and mappings acting as (anti-)homomorhism on non-zero ideal in prime rings are studied and the characterization of these mappings is given. In the fifth chapter, Xioa-Wei Xu and Hong-Ying Zhang' s work in 2011 is primarily considered. Derivations acting as (anti-)homomorphism on non-zero Jordan ideal in prime ring or on subring in prime ring are examined. In the sixth chapter, A. Al and Deepak Kumar' s work in 2009 is considered. Also, (θ,Φ)-derivations and left (θ,Φ)-derivations acting as (anti-)homomorphism on Jordan ideal and subring in prime or semi-prime rings are examined.