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On multiplicative (generalized) - derivations and central valued conditions in prime rings

Sandhu Gurninder S., Ayran Ayşe, Aydin Neşet

Journal of Mathematics and Applications

2021

Vol. 44

93--105

Let R be a prime ring with multiplicative (generalized)- derivations (F, f) and (G, g) on R. This paper gives a number of central valued algebraic identities involving F and G that are equivalent to the commutativity of R under some suitable assumptions. Moreover, in order to optimize our results, we show that the assumptions taken cannot be relaxed.

Semiprime near-rings with multiplicative generalized (θ,θ)-derivations

Koç E., Gölbaşi Ö.

Fasciculi Mathematici

2016

Nr 57

105--119

Let N be a semiprime right near-ring and I a semigroup ideal of N. A map f : N →N is called a multiplicative generalized (θ,θ)-derivation if there exists a multiplicative (θ,θ)-derivation d : R → such that f(xy) - f(x)θ(y) + θ(x)d(y), for all x,y ϵ R. The purpose of this paper is to investigate the following: [formula].