ON AGE RINGS AND AM MODULES WITH RELATED CONCEPTS

In this paper, all rings or (left)near-rings R are associative, and for near-ring R, all R-groups are right R action and all modules are right R-modules. First, we begin with the study of rings in which all the additive endomorphisms or only the left multiplication endomorphisms are generated by ring endomorphisms and their properties. This study was motivated by the work on the Sullivan's Problem [14]. Next, for any right R-module M, we will introduce AM modules and investigate their basic properties. Finally, for any nearring R, we will also introduce MR-groups and study some of their properties.