HIKARI Ltd, www.m-hikari.com Left R-prime (R, S)-submodules

Copyright c © 2013 T. Khumprapussorn. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We introduced (R,S)-modules as a generalization of bimodule struc-tures. Moreover, we presented the ways to study primalities of (R,S)-submodules, which we called fully prime and jointly prime (R,S)-submodules. In this paper, we define the third way to study primality of (R,S)-submodules, which we call left R-prime (R,S)-submodules. Charac-terizations and some properties of left R-prime submodules are also investigated