2023/11/17 by Saba Shirzadi, Shirzadi, Saba, R. Beyranvand +3
Mathematics · Neuroscience · #16D10 #16D60 #16D70 #16N20 #16S90 #Axon Guidance and Neuronal Signaling #FOS: Mathematics #G.m #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2311.10428
openalex publication_date 2023/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce and study a nontrivial generalization of uniserial modules and rings. A module is called weakly uniserial if its submodules are comparable regarding embedding. Also, a right (resp., left) weakly uniserial ring is a ring which is weakly uniserial as a right (resp., left) module over itself. In this paper, in addition to providing the properties of weakly uniserial modules and rings, we show that every right R-module is weakly uniserial if and only if every 2-generated right R-module is weakly uniserial, if and only if R is a simple Artinian ring. Then it is determined which torsion-free abelian groups of rank 1 are weakly uniserial. Finally, when R is a commutative principal ideal domain, the structure of finitely generated weakly uniserial R-modules are completely determined.