Modules with reduced endomorphism rings
Loading...
Date
2024-10-17
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
World Scientific Publishing
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.
Description
Keywords
Endo-reduced module, Reduced module, Endomorphism ring, Reduced ring, von Neumann regular ring
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