some results on strongly prime submodules
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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 $(p + rx : m)ysubseteq p$ 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 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.
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Journal title:
journal of algebraic systemsPublisher: shahrood university of technology
ISSN 2345-5128
volume 1
issue 2 2014
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