Journal of the
Korean Mathematical Society JKMS

In this paper, all rings and all near-rings $R$ are associative, all modules are right $R$-modules. For a near-ring $R,$ we consider representations of $R$ as $R$-groups. We start with a study of $AGR$ rings and their properties. Next, for any right $R$-module $M,$ we define a new concept $GM$ module and investigate the commutative property of faithful $GM$ modules and some characterizations of $GM$ modules. Similarly, for any near-ring $R,$ we introduce an $R$-group with $MR$-property and some properties of $MR$ groups.

Keywords: $AR$ rings, $AGR$ rings, $R$-homogeneous maps, centralizers, $GM$ modules, $MR$ groups

MSC numbers: Primary 16Y30, 16N40, 16S36