Let R be a Γ-ring and G be an RΓ-module. A proper RΓ-submodule S of G is said to be semiprime RΓ-submodule if for any ideal I of a Γ-ring R and for any RΓ-submodule A of G such that or which implies that . The purpose of this paper is to introduce interesting results of semiprime RΓ-submodule of RΓ-module which represents a generalization of semiprime submodules.

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Let R be a Γ-ring and G be a RΓ-module. Aproper RΓ-submodule E of G is said to be S-prime (S-semiprime) RΓ-submodule of G whenever μ(K) ⊆ E ( μ(m) γ μ(m) E ), for some K be a RΓ-submodule of G, where End (G), y Γ and m G, then K ⊆ E or M(G)⊆ E ( μ(m) E). The reason of this paper and we give some basic properties and characterizations of S-prime and S-semiprime submodules.

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