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arXiv · 2101.03333

Free Hom-groups, Hom-rings and Semisimple modules

Imed Basdouri·Sami Chouaibi·Abdenacer Makhlouf·Esmael Peyghan
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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.

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Imed Basdouri, Sami Chouaibi, Abdenacer Makhlouf, Esmael Peyghan. 2021-01-09. Free Hom-groups, Hom-rings and Semisimple modules. https://arxiv.org/abs/2101.03333

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