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Identities with generalized derivations in semiprime rings

Dhara B., Ali S., Pattanayak A.

Demonstratio Mathematica

2013

Vol. 46, nr 3

453--460

Let R be a semiprime ring. An additive mapping F:R  R is called a generalized derivation of R if there exists a derivation d : R  R such that F(xy) = F(x)y + xd(y) holds, for all x,y  R. The objective of the present paper is to study the following situations: (1) (...), for all x, y in some appropriate subset of R.

Identities with products of (alpha, beta)-derivations on prime rings

Vukman J.

Demonstratio Mathematica

2006

Vol. 39, nr 2

291-298

The main purpose of this paper is to prove the following result. Let R be a noncommutative prime ring of characteristic different from two and let D and G = 0 be (\alpha, beta)-derivations of R into itself such that G commutes with alpha and beta. If [D{x), G(x)] = 0 holds for all x is an eleemnt of R then D = lambdaG where lambda is an element from the extended centroid of R.