HIKARI Ltd, www.m-hikari.com A Generalization of Prime and

Copyright c © 2013 Adil Kadir Jabbar. 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. This paper presents two generalizations, one of prime submodules called S(N)−locally prime submodules and the other of weakly prime submodules called S(N)−weakly prime submodules. Several properties of prime and weakly prime submodules have been generalized to these new types of submodules and some characterizations of each type are given.