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Article

on special submodule of modules

a khaksari, s. mehri, r. safakish

Abstract

‎let $r$ be a domain with quotiont field $k$‎, ‎and‎ ‎let $n$ be a submodule of an $r$-module $m$‎. ‎we say that $n$ is‎ ‎powerful (strongly primary) if $x,yin k$ and‎ ‎$xymsubseteq n$‎, ‎then $xin r$ or $yin r$ ($xmsubseteq n$‎ ‎or $y^nmsubseteq n$ for some $ngeq1$)‎. ‎we show that a submodule‎ ‎with either of these properties is comparable to every prime‎ ‎submodule of $m$‎, ‎also we show that an $r$-module $m$ admits a‎ ‎powerful submodule if and only if it admits a strongly primary‎ ‎submodule‎. ‎finally we study finitely generated torsion free‎ ‎modules over domain each of whose prime submodules are strongly‎ ‎primary‎.

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