Second representable modules over commutative rings

被引：2

作者：

Abuhlail, Jawad ^{[1
]}

Hroub, Hamza ^{[2
]}

机构：

[1] King Fahd Univ Petr & Minerals, Dept Math & Stat, Dhahran 31261, Saudi Arabia

[2] King Saud Univ, Dept Math, Riyadh, Saudi Arabia

来源：

COMMUNICATIONS IN ALGEBRA | 2019年 / 47卷 / 09期

关键词：

Lifting modules; second attached prime ideals; second representations; second submodules; secondary representations; DECOMPOSITION;

D O I：

10.1080/00927872.2019.1572163

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a commutative ring. We investigate R-modules which can be written as finite sums of second R-submodules (we call them second representable). The class of second representable modules lies between the class of finitely generated semisimple modules and the class of representable modules; moreover, we give examples to show that these inclusions are strict even for Abelian groups. We provide sufficient conditions for an R-module M to be have a (minimal) second presentation, in particular within the class of lifting modules. Moreover, we investigate the class of (main) second attached prime ideals related to a module with such a presentation.

引用

页码：3859 / 3874

页数：16