annihilating submodule graphs for modules over commutative rings
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abstract
in this article, we give several generalizations of the concept of annihilating ideal graph over a commutative ring with identity to modules. weobserve that over a commutative ring $r$, $bbb{ag}_*(_rm)$ isconnected and diam$bbb{ag}_*(_rm)leq 3$. moreover, if $bbb{ag}_*(_rm)$ contains a cycle, then $mbox{gr}bbb{ag}_*(_rm)leq 4$. also for an $r$-module $m$ with$bbb{a}_*(m)neq s(m)setminus {0}$, $bbb{a}_*(m)=emptyset$if and only if $m$ is a uniform module and ann$(m)$ is a primeideal of $r$.
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Journal title:
journal of algebraic systemsPublisher: shahrood university of technology
ISSN 2345-5128
volume 3
issue 1 2015
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