Shahrood University of TechnologyJournal of Algebraic Systems2345-51281220140101SOME RESULTS ON STRONGLY PRIME SUBMODULES798922810.22044/jas.2014.228ENA.R. NaghipourDepartment of Mathematics, Shahrekord University, P.O.Box 115, Shahrekord,
Iran.0000-0002-7178-6173Journal Article20130411Let $R$ 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 <br />which is defined to be the length of a longest chain of strongly prime submodules.https://jas.shahroodut.ac.ir/article_228_6566623d100f92ad63091efa325975a1.pdf