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Fuzzy Small Submodule and Jacobson ð ¿ -Radical

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  • Saifur Rahman
  • Helen K. Saikia

Abstract

Using the notion of fuzzy small submodules of a module, we introduce the concept of fuzzy coessential extension of a fuzzy submodule of a module. We attempt to investigate various properties of fuzzy small submodules of a module. A necessary and sufficient condition for fuzzy small submodules is established. We investigate the nature of fuzzy small submodules of a module under fuzzy direct sum. Fuzzy small submodules of a module are characterized in terms of fuzzy quotient modules. This characterization gives rise to some results on fuzzy coessential extensions. Finally, a relation between small ð ¿ -submodules and Jacobson ð ¿ -radical is established.

Suggested Citation

  • Saifur Rahman & Helen K. Saikia, 2011. "Fuzzy Small Submodule and Jacobson ð ¿ -Radical," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-12, May.
    • Handle: RePEc:hin:jijmms:980320
    DOI: 10.1155/2011/980320
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