Torsion graph over multiplication modules

• Autores: Sh. Ghalandarzadeh, P. Malakooti Rad
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 24, Nº 3, 2009, págs. 281-299
• Idioma: inglés
• Enlaces
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• Resumen

  • For a commutative ring R, the torsion graph of an R-module M is ¡(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 n Z(M), then ¡(M) and ¡(S¡1M) are isomorphic for a multiplication R-module M. Also we prove that for a multiplication R-module M, if ¡(M) is uniquely complemented, then S¡1M is von Neumann regular or ¡(M) is a star graph