arXiv subjects

Saba Shirzadi

Publications and source records attributed to Saba Shirzadi.

2 recordsLinked to original sources

arXiv2026

Weakly uniserial dimension of modules

Recall that a module is called weakly uniserial if its submodules are comparable regarding embedding. Weakly uniserial modules are a nontrivial generalization of uniserial modules. In this paper we define and study a new dimension, which measure how far a module deviates from being weakly uniserial. We call this dimension, weakly uniserial dimension. Also, we define and study monoartinian (mononoetherian) modules. We say that an $R$-module $M$ is monoartinian (mononoetherian) if in every descending (ascending) chain of submodules of $M$, except probably a finite number, each module in chain embedded in the next (previous) one. We show that a module has weakly uniserial dimension if and only if it is monoartonian.

math.RA↗

arXiv2023

A generalization of uniserial modules and rings

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.

math.RA↗