1. Hypersimple Rings and Modules
- Author
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Lomp, Christian, Yousif, Mohamed, and Zhou, Yiqiang
- Subjects
Mathematics - Rings and Algebras ,16D40, 16D50, 16D60 (Primary), 16L30, 16L60, 16P20, 16P40, 16P60 (Secondary) - 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., Comment: dedicated to Andr\'e Leroy on his retirement
- Published
- 2023