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http://hdl.handle.net/10662/13008
Title: | Torsion graph of modules |
Authors: | Ghalandarzadeh, Shaban Malakooti Rad, Parastoo |
Keywords: | Torsion graph;Multiplication modules;Diameter of torsion graph;Gráfico de torsión;Módulos de multiplicación;Gráfico de diámetro de torsión |
Issue Date: | 2011 |
Publisher: | Universidad de Extremadura, Servicio de Publicaciones |
Abstract: | Let R be a commutative ring and M be an R-module. We associate to M a graph denoted by, Γ(M) called the torsion graph of M, whose vertices are the non-zero torsion elements of M and two distinct elements x; y are adjacent if and only if [x : M][y : M]M = 0. We investigate the interplay between module-theoretic properties of M and graph-theoretic properties of Γ(M). Among other results, we prove that Γ(M) is connected and diam(Γ(M)) ≤ 3 for a faithful R-module M. |
URI: | http://hdl.handle.net/10662/13008 |
ISSN: | 0213-8743 |
Appears in Collections: | Extracta Mathematicae Vol. 26, nº 1 (2011) |
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2605-5686_26_1_153.pdf | 99,23 kB | Adobe PDF | View/Open |
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