J. Aust. Math. Soc.  81 (2006), 225-243
Cotorsion modules and relative pure-injectivity

Lixin Mao
  Department of Basic Courses
  Nanjing Institute of Technology
  Nanjing 210013
  China
  and
  Department of Mathematics
  Nanjing University
  Nanjing 210093
  China
  maolx2@hotmail.com
and
Nanqing Ding
  Department of Mathematics
  Nanjing University
  Nanjing 210093, China
  nqding@nju.edu.cn


Abstract
Let $R$ be a ring. A right $R$-module $C$ is called a cotorsion module if $\operatorname{Ext}_{R}^{1}(F, C)=0$ for any flat right $R$-module $F$. In this paper, we first characterize those rings satisfying the condition that every cotorsion right (left) module is injective with respect to a certain class of right (left) ideals. Then we study relative pure-injective modules and their relations with cotorsion modules.
Download the article in PDF format (size 150 Kb)
Australian Mathematical Publishing Association Inc. ©  Australian MS