Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. A proper submodule $P$ of $M$ is called strongly prime submodule if $(P + Rx : M)ysubseteq P$ for $x, yin M$, implies that $xin P$ or $yin P$. In this paper, we study more properties of strongly prime submodules. It is shown that a finitely generated $R$-module $M$ is Artinian if and only if $M$ is Noetherian and every st...

 Prime submodules and artinian prime modules are characterized. Furthermore, some previous results on prime modules and second modules are generalized.

Our aim in this work is to investigate prime submodules and prove some properties of them. We study the relations between a given module extension submodules. The two modules direct product their quotient are studied investigated.