Fuzzy small submodule and Jacobson \(L\)-radical
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.
scientific article; zbMATH DE number 5900755
scientific article