On Modules Satisfying the Descending Chain Condition on Cyclic Submodules

• 作者: Farid Kourki Rachid Tribak
• 来源期刊: 代数集刊（英文版）
• 年，卷（期）: 2020,（3）
• 页码范围: 531-544
• 页数: 14页
• 语种: 英文
• DOI: 10.1142/S1005386720000449

摘要

A module satisfying the descending chain condition on cyclic submodules is called coperfect.The class of coperfect modules lies properly between the class of locally artinian modules and the class of semiartinian modules.Let R be a commutative ring with identity.We show that every semiartinian R-module is coperfect if and only if R is a T-ring.It is also shown that the class of coperfect R-modules coincides with the class of locally artinian R-modules if and only if m/m2 is a finitely generated R-module for every maximal ideal m of R.