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
Pages
11
From page
1441
To page
1451
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
Serial Year
2014
Journal title
Bulletin of the Iranian Mathematical Society
Record number
2358451
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