Generalizations of prime submodules over non-commutative rings - Emel Aslankarayigit Ugurlu (Journal of Hyperstructures)
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 ∅-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 Ø : 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 Ø-prime, if YI ⊆ X and YI ⊄ Ø(X); then Y ⊆ X or I ⊆ (X :R M): Then we examine the properties of Ø-prime submodules and characterize it when M is a multiplication module.