TY - JOUR ID - 228 TI - SOME RESULTS ON STRONGLY PRIME SUBMODULES JO - Journal of Algebraic Systems JA - JAS LA - en SN - 2345-5128 AU - Naghipour, A.R. AD - Department of Mathematics, Shahrekord University, P.O.Box 115, Shahrekord, Iran. Y1 - 2014 PY - 2014 VL - 1 IS - 2 SP - 79 EP - 89 KW - Prime submodule KW - classical Krull dimension KW - strongly prime submodule DO - 10.22044/jas.2014.228 N2 - 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. UR - https://jas.shahroodut.ac.ir/article_228.html L1 - https://jas.shahroodut.ac.ir/article_228_6566623d100f92ad63091efa325975a1.pdf ER -