On Representable Rings and Modules

被引：0

作者：

Mousavi, Seyed Ali ^{[1
]}

Mirzaei, Fatemeh ^{[1
]}

Nekooei, Reza ^{[1
]}

机构：

[1] Shahid Bahonar Univ Kerman, Mahani Math Res Ctr, Dept Pure Math, Kerman, Iran

来源：

KYUNGPOOK MATHEMATICAL JOURNAL | 2022年 / 62卷 / 03期

关键词：

Secondary modules; Secondary representation; Representable rings and modules; Laskerian rings and modules; Semiperfect rings; Artinian rings; Noethe-rian spectrum; Compactly packed rings; Q-rings; AB5* modules; Linearly compact mod-ules; LASKERIAN PROPERTY;

D O I：

10.5666/KMJ.2022.62.3.407

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we determine the structure of rings that have secondary repre-sentation (called representable rings) and give some characterizations of these rings. Also, we characterize Artinian rings in terms of representable rings. Then we introduce com-pletely representable modules, modules every non-zero submodule of which have secondary representation, and give some necessary and sufficient conditions for a module to be com-pletely representable. Finally, we define strongly representable modules and give some conditions under which representable module is strongly representable.

引用

页码：407 / 423

页数：17

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