Rocky Mountain Journal of Mathematics

On the graph of modules over commutative rings

H. Ansari-Toroghy and Sh. Habibi

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Let $M$ be a module over a commutative ring and let $\Spec (M)$ be the collection of all prime submodules of $M$. We topologize $\Spec (M)$ with quasi-Zariski topology and, for a subset $T$ of $\Spec (M)$, we introduce a new graph $G(\tau ^{*}_{T})$, called the \textit {quasi-Zariski topology-graph}. It helps us to study algebraic (respectively, topological) properties of $M$ (respectively, $\Spec (M)$) by using graph theoretical tools. Also, we study the annihilating-submodule graph and investigate the relation between these two graphs.

Article information

Rocky Mountain J. Math., Volume 46, Number 3 (2016), 729-747.

First available in Project Euclid: 7 September 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13C13: Other special types 13C99: None of the above, but in this section

Prime submodule top module quasi-Zariski topology graph vertices annihilating-submodule


Ansari-Toroghy, H.; Habibi, Sh. On the graph of modules over commutative rings. Rocky Mountain J. Math. 46 (2016), no. 3, 729--747. doi:10.1216/RMJ-2016-46-3-729.

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