Hypersimple Rings and Modules
Rings and Algebras
2023-02-09 v1
Abstract
In this paper a simple right R-module S over a ring R is called hypersimple if its injective hull E(S) is cyclic, and a ring R is called right hypersimple if every simple right R-module is hypersimple. We initiate a study of these new notions, and revisit Osofsky's work on hypercyclic rings, i.e. rings whose cyclic right modules have cyclic injective hulls.
Keywords
Cite
@article{arxiv.2302.03974,
title = {Hypersimple Rings and Modules},
author = {Christian Lomp and Mohamed Yousif and Yiqiang Zhou},
journal= {arXiv preprint arXiv:2302.03974},
year = {2023}
}
Comments
dedicated to Andr\'e Leroy on his retirement