• 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