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THE CONNECTED SUBGRAPH OF THE TORSION GRAPH OF A MODULE
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 Title & Authors
THE CONNECTED SUBGRAPH OF THE TORSION GRAPH OF A MODULE
Ghalandarzadeh, Shaban; Rad, Parastoo Malakooti; Shirinkam, Sara;
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 Abstract
In this paper, we will investigate the concept of the torsion-graph of an R-module M, in which the set makes up the vertices of the corresponding torsion graph, , with any two distinct vertices forming an edge if $[x:M][y:M]M
 Keywords
torsion graph;multiplication modules;von Neumann regular modules;
 Language
English
 Cited by
 References
1.
D. D. Anderson, Multiplication ideals, multiplication rings and the ring R(X), Canad. J. Math. 28 (1976), no. 4, 260-768.

2.
D. D. Anderson and M. Naseer, Beck's coloring of a commutative rings, J. Algebra 159 (1993), no. 2, 500-514. crossref(new window)

3.
D. F. Anderson, M. C. Axtell, and J. A. Stickles, Zero-divisor graphs in commutative rings, Commutative algebra, Noetherian and non-Noetherian perspectives, 23-45, Springer, New York, 2011.

4.
D. F. Anderson and A. Badawi, The total graph of a commutative ring, J. Algebra 320 (2008), no. 7, 2706-2719. crossref(new window)

5.
D. F. Anderson and A. Badawi, On the zero-divisor graph of a ring, Comm. Algebra 36 (2008), no. 8, 3073-3092. crossref(new window)

6.
D. F. Anderson, A. Frazier, A. Lauve, and P. S. Livingston, The zero-divisor graph of a commutative ring. II, Ideal theoretic methods in commutative algebra (Columbia, MO, 1999), 61-72, Lecture Notes in Pure and Appl. Math., 220, Dekker, New York, 2001.

7.
D. F. Anderson, R. Levy, and J. Shapiro, Zero-divisor graphs, von Neumann regular rings, and Boolean algebras, J. Pure Appl. Algebra 180 (2003), no. 3, 221-241. crossref(new window)

8.
D. F. Anderson and P. S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra 217 (1999), no. 2, 434-447. crossref(new window)

9.
A. Badawi and D. F. Anderson, Divisibility conditions in commutative rings with zero-divisors, Comm. Algebra 38 (2002), no. 8, 4031-4047.

10.
A. Barnard, Multiplication modules, J. Algebra 71 (1981), no. 1, 174-178. crossref(new window)

11.
I. Beck, Coloring of commutative rings, J. Algebra 116 (1988), no. 1, 208-226. crossref(new window)

12.
G. A. Cannon, K. Neuerburg, and S. P. Redmond, Zero-divisor graphs of nearrings and semigroups, Nearrings and nearfields, 189-200, Springer, Dordrecht, 2005.

13.
F. R. DeMeyer, T. McKenzie, and K. Schneider, The zero-divisor graph of a commutative semigroup, Semigroup Forum 65 (2002), no. 2, 206-214. crossref(new window)

14.
R. Diestel, Graph Theory, Springer-Verlag, New York, 1997.

15.
Z. A. El-Bast and P. F. Smith, Multiplication modules, Comm. Algebra 16 (1988), no. 4, 755-779. crossref(new window)

16.
SH. Ghalandarzadeh and P. Malakooti Rad, Torsion graph over multiplication modules, Extracta Math. 24 (2009), no. 3, 281-299.

17.
J. Han, The zero-divisor graph under group actions in a noncommutative ring, J. Korean Math. Soc. 45 (2008), no. 6, 1647-1659. crossref(new window)

18.
F. Kash, Modules and Rings, London: Academic Press, 1982.

19.
P. Malakooti Rad, Sh. Ghalandarzadeh, and S. Shirinkam, On the torsion graph and von Neumann regular rings, Filomat 26, 47-53. To appear.

20.
H. Matsumara, Commutative Ring Theory, Cambridge, UK: Cambridge University Press, 1986.

21.
S. P. Redmond, The zero-divisor graph of a non-commutative ring, Internat. J. Commutative Rings 1 (2002), no. 4, 203-211.

22.
P. Ribenboim, Algebraic Numbers, Wiley, 1972.