EP-内射性与环的von Neumann正则性

doi:10.6040/j.issn.1671-9352.0.2014.166

山东大学学报（理学版） ›› 2014, Vol. 49 ›› Issue (10): 33-37.doi: 10.6040/j.issn.1671-9352.0.2014.166

EP-内射性与环的von Neumann正则性

鲁琦¹, 殷晓斌², 鲍宏伟¹

1. 蚌埠学院数理系, 安徽蚌埠 233000;
2. 安徽师范大学数学与计算机科学学院, 安徽芜湖 241000

收稿日期:2014-04-21 出版日期:2014-10-20 发布日期:2014-11-10
作者简介:鲁琦(1980-),男,硕士,讲师,研究方向为环论.E-mail:luqi19801124@163.com
基金资助:
国家自然科学基金资助项目(11271016);安徽省自然科学基金资助项目(KJ2012Z300);蚌埠学院自然科学基金资助项目(2015ZR10)

EP-injectivity and von Neumann regularity of rings

LU Qi¹, YIN Xiao-bin², BAO Hong-wei¹

1. Department of Mathematics and Physics, Bengbu College, Bengbu 233000, Anhui, China;
2. College of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000, Anhui, China

Received:2014-04-21 Online:2014-10-20 Published:2014-11-10

摘要/Abstract

摘要： 给出了EP-内射环的一些等价定义,举例说明了EP-内射环未必是GP-内射环。证明了:若R是半完全的左EP-内射环,且Soc(_RR)在_RR中本质,则R是左,右Kasch环。

关键词: P-内射环, GP-内射环, von Neumann正则环, EP-内射环

Abstract: Some equivalent definitions of EP-injective rings are given. An example is given to show that EP-injective ring needs not be GP-injective. We prove that assume that R is semiperfect and left EP-injective. If Soc(_RR) is essential in _RR, then R is left and right Kasch.

Key words: P-injective ring, EP-injective ring, von-Neumann regular, GP-injective ring

中图分类号:

O153.3

鲁琦, 殷晓斌, 鲍宏伟. EP-内射性与环的von Neumann正则性[J]. 山东大学学报（理学版）, 2014, 49(10): 33-37.

LU Qi, YIN Xiao-bin, BAO Hong-wei. EP-injectivity and von Neumann regularity of rings[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(10): 33-37.

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EP-内射性与环的von Neumann正则性

EP-injectivity and von Neumann regularity of rings

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