Modules with reduced endomorphism rings
| dc.contributor.author | Kimuli, Philly Ivan | |
| dc.contributor.author | Ssevviiri, David | |
| dc.date.accessioned | 2025-01-07T07:13:55Z | |
| dc.date.available | 2025-01-07T07:13:55Z | |
| dc.date.issued | 2024-10-17 | |
| dc.description.abstract | In this paper, we study endo-reduced modules as modules whose endomorphism rings have no nonzero nilpotent elements. We characterize their properties for different classes of modules, including K-non-singular modules, multiplication modules and finitely generated modules over commutative Dedekind domains. In the subcategory of finitely generated modules, it is shown that the class of rings R for which every faithful multiplication R-module is endo-reduced is precisely that of reduced rings; while the class of rings R for which every multiplication R-module is endo-reduced is precisely that of von Neumann regular rings. Characterizations of when an endo-reduced module will be a reduced module are given. We prove that a finitely generated module over a principal ideal domain (PID) is endo-reduced exactly if it is either a semisimple module with pair-wise non-isomorphic submodules or a torsion-free module which is isomorphic to the underlying ring. | |
| dc.identifier.citation | Kimuli, P. I., & Ssevviiri, D. (2024). Modules with reduced endomorphism rings. Journal of Algebra and Its Applications, 2650042. https://doi.org/10.1142/S0219498826500428 | |
| dc.identifier.issn | 1793-6829 | |
| dc.identifier.uri | https://dir.muni.ac.ug/handle/20.500.12260/714 | |
| dc.language.iso | en | |
| dc.publisher | World Scientific Publishing | |
| dc.subject | Endo-reduced module | |
| dc.subject | Reduced module | |
| dc.subject | Endomorphism ring | |
| dc.subject | Reduced ring | |
| dc.subject | von Neumann regular ring | |
| dc.title | Modules with reduced endomorphism rings | |
| dc.type | Article |