Title of article :
On special submodule of modules
Author/Authors :
Khaksari، A. نويسنده Payame Noor University , , Mehry، S. نويسنده Bu ali sina University , , Safakish، R. نويسنده Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844, Islamic Republic of Iran ,
Issue Information :
دوماهنامه با شماره پیاپی سال 2014
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 $x,y\in K$ and
$xyM\subseteq N$, then $x\in R$ or $y\in R$ ($xM\subseteq N$
or $y^nM\subseteq N$ for some $n\geq1$). 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.
Journal title :
Bulletin of the Iranian Mathematical Society
Journal title :
Bulletin of the Iranian Mathematical Society