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2016 On the graph of modules over commutative rings
H. Ansari-Toroghy, Sh. Habibi
Rocky Mountain J. Math. 46(3): 729-747 (2016). DOI: 10.1216/RMJ-2016-46-3-729

Abstract

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.

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H. Ansari-Toroghy. Sh. Habibi. "On the graph of modules over commutative rings." Rocky Mountain J. Math. 46 (3) 729 - 747, 2016. https://doi.org/10.1216/RMJ-2016-46-3-729

Information

Published: 2016
First available in Project Euclid: 7 September 2016

zbMATH: 1369.13012
MathSciNet: MR3544833
Digital Object Identifier: 10.1216/RMJ-2016-46-3-729

Subjects:
Primary: 13C13, 13C99

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium

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Vol.46 • No. 3 • 2016
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