Semigroup ideals with multiplicative semiderivations and commutativity of 3-prime near-rings

Abstract

In the present paper, we introduce the notion of multiplicative semiderivation and prove some theorems in the setting of a semigroup ideal of a 3-prime near-ring admitting a multiplicative semiderivation. Thereby, it is shown that under appropriate additional hypotheses a near-ring must be a commutative ring. Furthermore, an example is given to illustrate that the 3-primeness hypothesis is not superfluous.