Fuzzy Small Submodule and Jacobson L-Radical

الملخص EN

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.