Skew derivations and b-generalized derivations
Project no. 20621 · Status: Kapanmış · 2019
Summary
In this work some identities involving special types of mappings (skew derivation ($\sigma$-derivation), $b$-generalized derivation) of prime rings are studied and the form of maps involved identities or the structure of the ring with these identities are characterized. This thesis essentially consists of six chapters. In the first chapter the subject of the thesis is introduced and the studies related to this subject are briefly summarized. The second chapter consists of basic definitions, properties and theorems which are essential for a better understanding of the problems to be studied in the following chapters of the thesis. In the third chapter, first of all, some of the studies that constitute this part and taken as motivation are mentioned and then by using tools of generalized polynomial identities theory, the annihilating condition of an identity involving skew derivation ($\sigma$-derivation) with Engel condition is studied. In the first part of fourth chapter, some identities involving different additive maps previously studied are extended to $b$-generalized derivation. In the second part, $b$-generalized derivations acting as a homomorphism or anti-homomorphism are examined. In the fifth chapter, the right (left) annihilating conditions and the central case of the identity that contains $b$-generalized derivation in prime rings are studied. Moreover, in the same chapter, the structure of the ring and the form of the mentioned maps are determined by considering an identity containing two different $b$-generalized derivations.