Some commutativity criteria for 3-prime near-rings

Abstract

In the present paper, we introduce the notion of \(*\)-generalized derivation in near-ring \(N\) and investigate some properties involving that of \(*\)-generalized derivation of a~\(*\)-prime near-ring \(N\) which forces \(N\) to be a~commutative ring. Some properties of generalized semiderivations have also been given in the context of 3-prime near-rings. Consequently, some well known results have been generalized. Furthermore, we will give examples to demonstrate that the restrictions imposed on the hypothesis of various results are not superfluous.