Annihilator Ideal-Based Zero-Divisor Graphs Over Multiplication Modules |
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Authors: | Ghalandarzadeh S. Shirinkam P. Malakooti Rad |
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Affiliation: | 1. Department of Mathematics , Faculty of Science, K. N. Toosi University of Technology , Tehran , Iran ghalandarzadeh@kntu.ac.ir;3. Department of Mathematics , Faculty of Science, K. N. Toosi University of Technology , Tehran , Iran;4. Faculty of Electronic and Computer and IT Islamic Azad University Qazvin Branch , Qazvin , Iran |
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Abstract: | For a commutative ring R with identity, an ideal-based zero-divisor graph, denoted by Γ I (R), is the graph whose vertices are {x ∈ R?I | xy ∈ I for some y ∈ R?I}, and two distinct vertices x and y are adjacent if and only if xy ∈ I. In this article, we investigate an annihilator ideal-based zero-divisor graph by replacing the ideal I with the annihilator ideal Ann(M) for a multiplication R-module M. Based on the above-mentioned definition, we examine some properties of an R-module over a von Neumann regular ring, and the cardinality of an R-module associated with Γ Ann(M)(R). |
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Keywords: | Annihilator ideal-based zero-divisor graphs Multiplication modules Von Neumann regular rings |
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