Primalities of (R,S)-Submodules Of (R,S)-Modules and of left multiplication (R,S)-Modules

Abstract

In this research, the notions of (R, S)-modules and left multiplication (R, S)-modules are introduced. We define and investigate fully prime (R, S)-submodules, jointly prime (R, S)-submodules and left R-prime (R, S)-submodules. Fully prime (R, S)-submodules and jointly prime (R, S)-submodules of a left multiplication (R, S)-module are shown to be identical. Moreover, characterizations of fully prime (R, S)-submodules, jointly prime (R, S)-submodules and left R-prime (R, S)-submodules of an (R, S)-module and of a left multiplication (R, S)-module are provided.