Kimuli, Philly IvanSsevviiri, David2025-01-072025-01-072024-10-17Kimuli, P. I., & Ssevviiri, D. (2024). Modules with reduced endomorphism rings. Journal of Algebra and Its Applications, 2650042. https://doi.org/10.1142/S02194988265004281793-6829https://dir.muni.ac.ug/handle/20.500.12260/714In 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.enEndo-reduced moduleReduced moduleEndomorphism ringReduced ringvon Neumann regular ringArticle