遗传挠理论的余投射模和余内射模

J4 ›› 2011, Vol. 49 ›› Issue (03): 412-418.

遗传挠理论的余投射模和余内射模

张力宏¹, 杜奕秋^1,2

1. 吉林师范大学数学学院, 吉林四平 136000|2. 吉林大学数学研究所, 长春 130012

收稿日期:2010-06-29 出版日期:2011-05-26 发布日期:2011-06-15
通讯作者: 杜奕秋 E-mail:duyiqiu2006@163.com.

Co-projective Modules and Coinjective Modules Relatedto the Hereditary Torsion Theory

ZHANG Lihong¹, DU Yiqiu^1,2

1. College of Mathematics, Jilin Normal University, Siping 136000, Jilin Province, China;2. Institute of Mathematics, Jilin University, Changchun 130012, China

Received:2010-06-29 Online:2011-05-26 Published:2011-06-15
Contact: DU Yiqiu E-mail:duyiqiu2006@163.com.

摘要/Abstract

摘要：

通过给出关于遗传挠理论的余投射模和余内射模的概念, 证明了这两类模的一些等价命题, 并揭示了这两类模的对偶性; 利用关于遗传挠理论的余投射模给出了余半单环和余左遗传环的概念, 并研究了这两类环的结构.

关键词: τ余内射模, τ余投射模, τ挠模, τ挠自由模

Abstract:

The authors presented the concepts of co-projective modules and co-injective modules related to the hereditary torsion theory and proved some equivalent conditions of these two types of modules, revealed the duality of these two types of modules, gave the concepts of co-semisimple rings and left co-hereditary rings by means of co-projective module related to the hereditary torsion theory and studied the structure of these two types of rings.

Key words: τcoinjective module, τcoprojective module, τtorsionmodule, τtorsion free module

中图分类号:

O153

张力宏, 杜奕秋. 遗传挠理论的余投射模和余内射模[J]. J4, 2011, 49(03): 412-418.

ZHANG Li-Hong, DU Yi-Qiu. Co-projective Modules and Coinjective Modules Relatedto the Hereditary Torsion Theory[J]. J4, 2011, 49(03): 412-418.