Communications of the
Korean Mathematical Society CKMS

Throughout this paper, we will consider that $R$ is a near-ring and $G$ an $R$-group. We initiate the study of monogenic, strongly monogenic $R$-groups, 3 types of nonzero $R$-groups and their basic properties. At first, we investigate some properties of D.G. $(R,S)$-groups, faithful $R$-groups, monogenic $R$-groups, simple and $R$-simple $R$-groups. Next, we introduce modular right ideals, $t$-modular right ideals and 3 types of primitive near-rings. The purpose of this paper is to investigate some properties of primitive types near-rings and their characterizations.

Keywords: simple, $R$-simple, monogenic, strongly monogenic, faithful $R$-groups, D.G. $(R,S)$-group, 3 types of $R$-groups, modular right ideals, $t$-modular right ideals and 3 types of primitive near-rings

MSC numbers: Primary 16Y30