2022/08/16 by R. Nikandish, Nikandish, R., M. J. Nikmehr +3
Computer Science · Mathematics · #Advanced Algebra and Logic #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2208.07940
openalex publication_date 2022/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An R-module M is called virtually uniserial if for every finitely generated submodule 0 ≠ K ⊆ M, K/Rad(K) is virtually simple. In this paper, we generalize virtually uniserial modules by dropping the virtually simple condition and replacing it by the cyclic uniform condition. An R-module M is called cyclic-uniform uniserial if K/Rad(K) is cyclic and uniform, for every finitely generated submodule 0 ≠ K ⊆ M. Also, M is said to be cyclic-uniform serial if it is a direct sum of cyclic-uniform uniserial modules. Several properties of cyclic-uniform (uni)serial modules and rings are given. Moreover, the structure of Noetherian left cyclic-uniform uniserial rings are characterized. Finally, we study rings R have the property that every finitely generated R-module is cyclic-uniform serial.