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Cotorsion modules and relative pure-injectivity

Part of: Modules, bimodules and ideals Homological methods

Published online by Cambridge University Press:  09 April 2009

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

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Let R be a ring. A right R-module C is called a cotorsion module if Ext1R (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.

Keywords

cotorsion modulerelative pure-injective modulePS ringuniversally mininjective ringpure-V-ring.

MSC classification

Secondary: 16D50: Injective modules, self-injective rings 16E50: von Neumann regular rings and generalizations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 81 , Issue 2 , October 2006 , pp. 225 - 244
Copyright
Copyright © Australian Mathematical Society 2006

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