On special submodule of modules
Authors
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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Journal title
volume 40 issue 6
pages 1441- 1451
publication date 2014-12-01
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