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Title: Torsion graph over multiplication modules
Authors: Ghalandarzadeh, Sh.
Malakooti Rad, P.
Keywords: Torsion graph;Multiplication module;Von Neumann regular module;Gr谩fico de torsi贸n;M贸dulo de multiplicaci贸n;M贸dulo regular de Von Neumann
Issue Date: 2009
Publisher: Universidad de Extremadura, Servicio de Publicaciones
Abstract: For a commutative ring R, the torsion graph of an R-module M is 饾洡 (M) whose vertices are nonzero torsion elements of M, and two distinct vertices x and y are adjacent if and only if [x: M] [y: M ]M = 0. In this article we show that if S = R \ Z (M), then 饾洡 (M) and 饾洡 (S鈦宦筂) are isomorphic for a multiplication R-module M. Also we prove that for a multiplication R-module M, if (饾洡 M) is uniquely complemented, then S鈦宦筂 is von Neumann regular or 饾洡 (M) is a star graph.
ISSN: 0213-8743
Appears in Collections:Extracta Mathematicae Vol. 24, n潞 3 (2009)

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