  The purpose of this paper is to introduce and study a Hom-type generalization
of rings. We provide their basic properties and and some key constructions.
Furthermore, we consider modules over Hom-rings and characterize the category
of simple modules and simple Hom-rings. In addition, we extend some classical
results and concepts of groups to Hom-groups. We construct free regular
Hom-group using Super-Leaf weighted trees and discuss Normal Hom-subgroups,
abelianization of regular Hom-group, universality of tensor product of
Hom-groups and simple Hom-groups.
