Fuzzy semimaximal submodules

الملخص EN

Let R be a commutative ring with unity and an R-submodule N is called semimaximal if and only if M/N is a semisimple R-module.

The main object of this work is to fuzzy this concept, study the basic properties and we investigate the sufficient conditions of F-submodules to be semimaximal.

Also, the concepts of (simple, semisimple) F- submodules and quotient F- modules are introduced and given some properties.