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.