Resumen de Torsion graph over multiplication modules

Sh. Ghalandarzadeh, P. Malakooti Rad

• 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