Free Hom-groups, Hom-rings and Semisimple modules
Rings and Algebras
2021-01-12 v1 Group Theory
Abstract
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.
Cite
@article{arxiv.2101.03333,
title = {Free Hom-groups, Hom-rings and Semisimple modules},
author = {Imed Basdouri and Sami Chouaibi and Abdenacer Makhlouf and Esmael Peyghan},
journal= {arXiv preprint arXiv:2101.03333},
year = {2021}
}