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.
similar resources
On special submodule of modules
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 tha...
full textModules for which every non-cosingular submodule is a summand
A module $M$ is lifting if and only if $M$ is amply supplemented and every coclosed submodule of $M$ is a direct summand. In this paper, we are interested in a generalization of lifting modules by removing the condition"amply supplemented" and just focus on modules such that every non-cosingular submodule of them is a summand. We call these modules NS. We investigate some gen...
full textAnnihilating Submodule Graphs for Modules over Commutative Rings
In this article, we give several generalizations of the concept of annihilating an ideal graph over a commutative ring with identity to modules. We observe that, over a commutative ring, R, AG∗(RM) is connected, and diamAG∗(RM) ≤ 3. Moreover, if AG∗(RM) contains a cycle, then grAG∗(RM) ≤ 4. Also for an R-module M with A∗(M) ̸= S(M) \ {0}, A∗(M) = ∅, if and only if M is a uniform module, and ann(...
full textdedekind modules and dimension of modules
در این پایان نامه، در ابتدا برای مدول ها روی دامنه های پروفر شرایط معادل به دست آورده ایم و خواصی از ددکیند مدول ها روی دامنه های پروفر مشخص کرده ایم. در ادامه برای ددکیند مدول های با تولید متناهی روی حلقه های به طور صحیح بسته شرایط معادل به دست آورده ایم و ددکیند مدول های ضربی را مشخص کرده ایم. گزاره هایی در مورد بعد ددکیند مدول ها بیان کرده ایم. در پایان، قضایای lying over و going down را برا...
15 صفحه اولA Submodule-Based Zero Divisors Graph for Modules
Let $R$ be commutative ring with identity and $M$ be an $R$-module. The zero divisor graph of $M$ is denoted $Gamma{(M)}$. In this study, we are going to generalize the zero divisor graph $Gamma(M)$ to submodule-based zero divisor graph $Gamma(M, N)$ by replacing elements whose product is zero with elements whose product is in some submodules $N$ of $M$. The main objective of this pa...
full textMy Resources
Save resource for easier access later
Journal title:
bulletin of the iranian mathematical societyPublisher: iranian mathematical society (ims)
ISSN 1017-060X
volume 40
issue 6 2014
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023