%0 Journal Article %T SOME RESULTS ON STRONGLY PRIME SUBMODULES %J Journal of Algebraic Systems %I Shahrood University of Technology %Z 2345-5128 %A Naghipour, A.R. %D 2014 %\ 01/01/2014 %V 1 %N 2 %P 79-89 %! SOME RESULTS ON STRONGLY PRIME SUBMODULES %K Prime submodule %K classical Krull dimension %K strongly prime submodule %R 10.22044/jas.2014.228 %X 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 $(P + Rx : M)y P$ for $x, y M$, implies that $x P$ or $y P$. 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 strongly prime submodule of $M$ is maximal. We also study the strongly dimension of a module which is defined to be the length of a longest chain of strongly prime submodules. %U https://jas.shahroodut.ac.ir/article_228_6566623d100f92ad63091efa325975a1.pdf