Principal ideal multiplication modules

被引：7

作者：

Azizi, A. ^{[1
]}

机构：

[1] Shiraz Univ, Coll Sci, Dept Math, Shiraz 71454, Iran

来源：

ALGEBRA COLLOQUIUM | 2008年 / 15卷 / 04期

关键词：

multiplication modules; prime submodules; principal ideal multiplication modules; semi-non-torsion modules;

D O I：

10.1142/S1005386708000606

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let M be an R-module. If for every sub module N of M; there exists an element r epsilon R such that N=rM; then we say that M is a principal ideal multiplication module. In this paper, the relations between principal ideal multiplication modules, multiplication modules, cyclicmodules, and modules over principal ideal rings are studied. It is proved that every principal ideal multiplication module over any quotient of a Dedekind domain iscyclic. Also, every principal ideal multiplication module with prime annihilator ideal is cyclic.

引用

页码：637 / 648

页数：12

共 17 条

[1] Some remarks on multiplication ideals, II [J].