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Almost Cotorsion Modules

Almost Cotorsion Modules
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摘要 In this paper, we introduce the concept of almost cotorsion modules. A module is called almost cotorsion if it is subisomorphic to its cotorsion envelope. Some characterizations of almost cotorsion modules are given. It is also proved that every module is a direct summand of an almost cotorsion module. As an application, perfect rings are characterized in terms of almost cotorsion modules. In this paper, we introduce the concept of almost cotorsion modules. A module is called almost cotorsion if it is subisomorphic to its cotorsion envelope. Some characterizations of almost cotorsion modules are given. It is also proved that every module is a direct summand of an almost cotorsion module. As an application, perfect rings are characterized in terms of almost cotorsion modules.
作者 毛立新
出处 《Northeastern Mathematical Journal》 CSCD 2006年第1期67-72,共6页 东北数学(英文版)
基金 Specialized Research Fund (20050284015, 20030284033) for the Doctoral Program of Higher Education of China the Postdoctoral Research Fund (2005037713) of China Jiangsu Planned Projects for Postdoctoral Research Fund (0203003403) the Research Fund of Nanjing Institute of Technology of China
关键词 cotorsion module almost cotorsion module perfect ring ENVELOPE cotorsion module, almost cotorsion module, perfect ring, envelope
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