Fuzzy Small Submodule and Jacobson ð ¿ -Radical

Saifur Rahman and Helen K. Saikia

International Journal of Mathematics and Mathematical Sciences, 2011, vol. 2011, 1-12

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.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:980320

DOI: 10.1155/2011/980320

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