On commutative rings whose maximal ideals are idempotent

被引：0

作者：

Kourki, Farid ^{[1
]}

Tribak, Rachid ^{[2
]}

机构：

[1] Ctr Reg Metiers Educ & Format CRMEF Tanger, BP 4063, Larache, Morocco

[2] Ctr Reg Metiers Educ & Format CRMEF Tanger, Ave My Abdelaziz,BP 3117, Tangier, Morocco

来源：

COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE | 2019年 / 60卷 / 03期

关键词：

artinian module; modules of finite length; noetherian module; quasiinjective module; quasi-projective module; radical-fine class of modules; soclefine class of modules; MODULES;

D O I：

10.14712/1213-7243.2019.012

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that for a commutative ring R, every noetherian (artinian) R-module is quasi-injective if and only if every noetherian (artinian) R-module is quasi-projective if and only if the class of noetherian (artinian) R-modules is socle-fine if and only if the class of noetherian (artinian) R-modules is radical-fine if and only if every maximal ideal of R is idempotent.

引用

页码：313 / 322

页数：10

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