Volume 10, Issue 1 (4-2015)                   IJMSI 2015, 10(1): 45-58 | Back to browse issues page

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Abbasi A, Roshan-Shekalgourabi H, Hassanzadeh-Lelekaami D. Associated Graphs of Modules Over Commutative Rings. IJMSI 2015; 10 (1) :45-58
URL: http://ijmsi.ir/article-1-418-en.html
Associated Graphs of Modules Over Commutative Rings
A. Abbasi , H. Roshan-Shekalgourabi , D. Hassanzadeh-Lelekaami
Abstract:  
Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. In this paper we introduce a new graph associated to modules over commutative rings. We study the relationship between the algebraic properties of modules and their associated graphs. A topological characterization for the completeness of the special subgraphs is presented. Also modules whose associated graph is complete, tree or complete bipartite are studied and several characterizations are given.
Keywords: Associated Graph of module, Prime spectrum, Connected graph, Diameter.
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Type of Study: Research paper | Subject: Special
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