Nearly prime GR-submodules of GR-modules

Abstract

A gamma ring(Γ− ring) is ΓR-module and W is proper ΓR-submodule. Let W be a proper ΓR-submodule of an ΓR-module is called nearly prime, for short N-P.ΓR-submodule if whenever and rγ m ∈ W implies that either or where is the Jacobson radical of . The goal of this work is to offer an intriguing way of defining and studying nearly P.ΓR-submodule of ΓR-module, for short N-P.ΓR-submodule of ΓR-module result N-P.ΓR-submodule of ΓR-module which represent generalization N-prime submodules.