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- W4288045452 abstract "Let R be a commutative ring with identity, and let M be an R-module. In this paper, we focus on the ideals of R that are annihilators of torsion elements of M. In analogy with definitions and results on zero-divisor and annihilator graphs of rings, we define the annihilator graph of a module. We investigate the structure, the diameter, and the girth of this graph and the closely related torsion graph of a module introduced by Ghalandarzadeh and Malakooti Rad. Given the right definitions, the properties of the modules are reflected in the graph theoretic properties of the graphs. We thus modify and extend results on zero divisors of rings to the much more general setting of modules and their torsion elements. In addition, we significantly strengthen the known results on the torsion graphs of modules. Some of the results will be refined further for the cases when M is a multiplication module or a reduced module." @default.
- W4288045452 created "2022-07-27" @default.
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- W4288045452 date "2022-11-01" @default.
- W4288045452 modified "2023-09-25" @default.
- W4288045452 title "On torsion elements and their annihilators" @default.
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- W4288045452 doi "https://doi.org/10.1016/j.jalgebra.2022.07.009" @default.
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