@article {
author = {Naghipour, A.R.},
title = {SOME RESULTS ON STRONGLY PRIME SUBMODULES},
journal = {Journal of Algebraic Systems},
volume = {1},
number = {2},
pages = {79-89},
year = {2014},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2014.228},
abstract = {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.},
keywords = {Prime submodule,classical Krull dimension,strongly prime submodule},
url = {https://jas.shahroodut.ac.ir/article_228.html},
eprint = {https://jas.shahroodut.ac.ir/article_228_6566623d100f92ad63091efa325975a1.pdf}
}