generalizations of prime submodules over non-commutative rings

Throughout this paper, r is an associative ring (not necessarily commutative) with identity and m is a right r-module with unitary. in this paper, we introduce a new concept of empty;-prime submodule over an associative ring with identity. thus we define the concept as following: assume that s(m) is the set of all submodules of m and oslash; : s(m) ! s(m) [ f;g is a function. for every y 2 s(m) and ideal i of r; a proper submodule x of m is called oslash;-prime, if yi sube; x and yi nsub; oslash;(x); then y sube; x or i sube; (x :r m): then we examine the properties of oslash;-prime submodules and characterize it when m is a multiplication module.