Identities with generalized derivations in semiprime rings

Generalized Derivations in Semiprime Gamma Rings

Identities with derivations and automorphisms on semiprime rings

The purpose of this paper is to investigate identities with derivations and automorphisms on semiprime rings. A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative. Mayne proved that in case there exists a nontrivial centralizing automorphism on a prime ring, then the ring is commutative. In this paper, some...

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

Lie Ideals and Generalized Derivations in Semiprime Rings

Let R be a 2-torsion free ring and L a Lie ideal of R. An additive mapping F : R ! R is called a generalized derivation on R if there exists a derivation d : R to R such that F(xy) = F(x)y + xd(y) holds for all x y in R. In the present paper we describe the action of generalized derivations satisfying several conditions on Lie ideals of semiprime 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 ...