A Generalization of Hopkins-Levitzki Theorem

被引：0

作者：

Le Phuong-Thao ^{[1
,2
]}

Nguyen Van Sanh ^{[3
]}

机构：

[1] Mahidol Univ, Dept Math, Bangkok 10400, Thailand

[2] Can Tho Univ, Can Tho, Vietnam

[3] Mahidol Univ, Dept Math, Ctr Excellence Math, Bangkok, Thailand

来源：

SOUTHEAST ASIAN BULLETIN OF MATHEMATICS | 2013年 / 37卷 / 04期

关键词：

Prime submodule; Semiprime submodule; Prime radical; Nilpotent submodule;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Hopkin-Levitzki theorem said that every right Artinian ring is right Noetherian. It is well-knnown that not every Artinian is Noetherian, for example the Prufer group Z(p infinity) is Artinian but not Noetherian. In this paper, we prove that if M is an Artinian quasi-projective finitely generated right R-module which is a self-generator, then it is Noetherian. This result can be considered as a generalization of Hopkins-Levitzki Theorem.

引用

页码：591 / 600

页数：10

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