On Semi(prime) Rings and Algebras with Automorphisms and Generalized Derivations
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Let R be a ring. An additive mapping \(F : R\rightarrow R\) is called a generalized derivation if there exists a derivation \(d : R\rightarrow R \) such that \( F(x y) = F(x)y + xd(y)\) for all \( x, y \in R\). In this paper, first we describe the structure of prime rings involving automorphisms and then characterized generalized derivations on semiprime rings which satisfy certain differential identities. As applications, and apart from proving the other results, many known theorems can be either generalized or deduced. Moreover, we apply our results to functional analysis, and to study the analogous conditions for continuous linear generalized derivations on Banach algebras.
Keywords(Semi)prime ring Banach algebra Automorphism Derivation Generalized derivation
Mathematics Subject Classification16W25 16N60 16U80 46J45
The authors are grateful to the learned referee(s) for his/her carefully reading the manuscript. The valuable suggestions and comments have simplified and clarified the paper immensely.
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