On Commutativity of Semiprime Rings with Multiplicative (Generalized)-derivations

On Generalized Derivations of Semiprime Rings

Let F be a commuting generalized derivation, with associated derivation d, on a semiprime ring R. We show that d(x)[y, z] = 0 for all x, y, z ∈ R and d is central. We define and characterize dependent elements of F and investigate a decomposition of R relative to F . Mathematics Subject Classification: 16N60, 16W25

On Jordan generalized k-derivations of semiprime Γ_N-Rings

Generalized Derivations on Semiprime Gamma Rings with Involution

An extensive generalized concept of classical ring set forth the notion of a gamma ring theory. As an emerging field of research, the research work of classical ring theory to the gamma ring theory has been drawn interest of many algebraists and prominent mathematicians over the world to determine many basic properties of gamma ring and to enrich the world of algebra. The different researchers ...

Generalized Derivations in Semiprime Gamma Rings

On Generalized Derivations and Commutativity of Prime Rings with Involution

Let R be a ring with involution ′∗′. A map δ of the ring R into itself is called a derivation if δ(xy) = δ(x)y + xδ(y) for all x, y ∈ R. An additive map F : R → R is called a generalized derivation on R if F(xy) = F(x)y + xδ(y) for all x, y ∈ R, Permanent address: Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh202002, India 292 Shakir Ali and Husain Alhazmi whe...