|
|||||
|
|
Euclidean modules |
|
| Authors: | Jichun Liu Miaosen Chen |
| Institution: | 1. Zhejiang University, Zhejiang, China 3. Fujian Jiangxia University, Fujian, China 2. Zhejiang Normal University, Zhejiang, China |
| Abstract: | In this paper, we introduce the notion of Euclidean module and weakly Euclidean ring. We prove the main result that a commutative ring R is weakly Euclidean if and only if every cyclic R-module is Euclidean, and also if and only if End( R M) is weakly Euclidean for each cyclic R-moduleM. In addition, some properties of torsion-free Euclidean modules are presented. |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ | |