On commutativity conditions of gamma rings

The aim of this study is to investigate what can be said about the commutativity of rings and gamma rings by making use of maps that provide some identity in these structures. In this direction, the thesis is basically composed of four chapters. In the first chapter, some studies investigating the commutativity conditions in rings and gamma rings in the literature are mentioned. In the second chapter, some basic definitions and properties that will make it easier to read the thesis is given. For this purpose, the definitions of the ring and the gamma ring are given, and the ideals of these structures that provide certain properties and the maps that provide some identities on these structures are introduced. In the third chapter, the paper of H. E. Bell and M. N. Daif, published in 1994, entitled "On commutativity and strong commutativity preserving maps" is examined in detail. In the fourth chapter, the paper of X. Xu, J. Ma and Y. Zhou published in 2015, entitled "Left derivations and strong commutativity preserving maps on semiprime Γ-rings" are discussed.