On Regular Modules over Commutative Rings

  • Dawood Hassanzadeh-LelekaamiEmail author
  • Hajar Roshan-Shekalgourabi


In this paper, we investigate the class of von Neumann regular modules over commutative rings. More precisely, we introduce a characterization of regular modules, and then, we study some properties of these modules in viewpoint of this characterization. Among other things, we show that the Nakayama’s Lemma and Krull’s intersection theorem hold for this class of modules. Also, some explicit expressions for submodules of regular modules are introduced.


Von Neumann regular ring Regular module Semisimple module Krull’s intersection theorem Prime submodule 

Mathematics Subject Classification

16E50 13C13 13C05 16D40 16D60 13C11 



The authors specially thank the referee for the helpful suggestions and comments.


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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2017

Authors and Affiliations

  • Dawood Hassanzadeh-Lelekaami
    • 1
    Email author
  • Hajar Roshan-Shekalgourabi
    • 1
  1. 1.Department of Basic SciencesArak University of TechnologyArakIran

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