Strongly lifting modules and strongly dual Rickart modules

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• 作者：Yongduo Wang
• 关键词：Lifting module ; strongly lifting module ; dual Rickart module ; strongly dual Rickart module
• 刊名：Frontiers of Mathematics in China
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：12
• 期：1
• 页码：219-229
• 全文大小：146 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Chinese Library of Science
  
• 出版者：Higher Education Press, co-published with Springer-Verlag GmbH
• ISSN：1673-3576
• 卷排序：12

文摘

The concepts of strongly lifting modules and strongly dual Rickart modules are introduced and their properties are studied and relations between them are given in this paper. It is shown that a strongly lifting module has the strongly summand sum property and the generalized Hopfian property, and a ring R is a strongly regular ring if and only if R_R is a strongly dual Rickart module, if and only if aR is a fully invariant direct summand of R_R for every a ∈ R.