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-Regular Modules

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  • Areej M. Abduldaim
  • Sheng Chen

Abstract

We introduced and studied -regular modules as a generalization of -regular rings to modules as well as regular modules (in the sense of Fieldhouse). An -module is called -regular if for each and , there exist and a positive integer such that . The notion of -pure submodules was introduced to generalize pure submodules and proved that an -module is -regular if and only if every submodule of is -pure iff is a -regular -module for each maximal ideal of . Many characterizations and properties of -regular modules were given. An -module is -regular iff is a -regular ring for each iff is a -regular ring for finitely generated module . If is a -regular module, then .

Suggested Citation

  • Areej M. Abduldaim & Sheng Chen, 2013. "-Regular Modules," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, March.
    • Handle: RePEc:hin:jnljam:630285
    DOI: 10.1155/2013/630285
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