Fuzzy Semimaximal Submodules

Abstract

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

Keywords

• Let R be a commutative ring with unity and an R-submodule N is called semimaximal if and only if M⁄(Nis a semisimple R-module ).The main objective of this work is to fuzzify 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 .