PRIME SUBMODULES IN EXTENDED BCK-MODULE

Abstract

In this paper, by considering the notion of BCK-module, we define the concept of extended BCK-module which is a generalization of BCK-module and we state and prove some related results.  Specially, we define the notions of prime submodule and torsion free module and we investigate some important results.  Finally, we define the concept of radical of any submodule in extended BCK-modules and we characterize the elements of it.