Fuzzy small submodule and Jacobson \(L\)-radical (Q539415)
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scientific article; zbMATH DE number 5900755
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fuzzy small submodule and Jacobson \(L\)-radical |
scientific article; zbMATH DE number 5900755 |
Statements
Fuzzy small submodule and Jacobson \(L\)-radical (English)
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27 May 2011
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Summary: 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 \(L\)-submodules and Jacobson \(L\)-radical is established.
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