论文标题
循环均匀的单性模块和环
Cyclic-Uniform Uniserial Modules and Rings
论文作者
论文摘要
如果每个有限生成的子模块$ 0 \ neq k \ subseteq m $，$ k/$ k/$ rad $（k）$，几乎很简单，则$ r $ -MODULE $ M $几乎是单性的。在本文中，我们通过删除几乎简单的条件并通过循环统一条件代替它来概括几乎单性模块。如果$ k/$ rad $（k）$是循环且均匀的，则$ r $ -MODULE $ M $称为环状均匀单层，对于每个有限生成的subpodule $ 0 \ neq k \ subseteq m $。另外，如果$ m $是循环均匀的串行序列，则是循环均匀的单性模块的直接总和。给出了循环均匀（UNI）串行模块和环的几种特性。此外，表征了Noetherian左循环均匀的单层环的结构。最后，我们研究戒指$ r $具有每个有限生成的$ r $ module的属性。
An $R$-module $M$ is called virtually uniserial if for every finitely generated submodule $0 \neq K \subseteq M$, $K/$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 $0 \neq K \subseteq M$. 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.
