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The total torsion element graph of a module over a commutative ring. (English) Zbl 1224.13004

Summary: The total graph of a commutative ring have been introduced and studied by D. F. Anderson and A. Badawi [J. Algebra 320, No. 7, 2706–2719 (2008; Zbl 1158.13001)]. In a manner analogous to a commutative ring, the total torsion element graph of a module \(M\) over a commtative ring \(R\) can be defined as the undirected graph \(T(\Gamma(M))\). The basic properties and possible structures of the graph \(T(\Gamma(M))\) are studied. The main purpose of this paper is to extend the definition and some results given in [loc. cit.] to a more general total torsion element graph case.

MSC:

13A15 Ideals and multiplicative ideal theory in commutative rings
05C75 Structural characterization of families of graphs

Citations:

Zbl 1158.13001
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