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AUTOMORPHISMS OF THE ZERO-DIVISOR GRAPH OVER 2 × 2 MATRICES
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 Title & Authors
AUTOMORPHISMS OF THE ZERO-DIVISOR GRAPH OVER 2 × 2 MATRICES
Ma, Xiaobin; Wang, Dengyin; Zhou, Jinming;
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 Abstract
The zero-divisor graph of a noncommutative ring R, denoted by , is a graph whose vertices are nonzero zero-divisors of R, and there is a directed edge from a vertex x to a distinct vertex y if and only if xy
 Keywords
automorphism;zero-divisor graph;noncommutative ring;matrix ring;
 Language
English
 Cited by
1.
Automorphisms of the zero-divisor graph of the full matrix ring, Linear and Multilinear Algebra, 2016, 1  crossref(new windwow)
2.
Automorphism group of the total graph over a matrix ring, Linear and Multilinear Algebra, 2016, 1  crossref(new windwow)
 References
1.
S. Akbari and A. Mohammadian, Zero-divisor graphs of non-commutative rings, J. Algebra 296 (2006), no. 2, 462-479. crossref(new window)

2.
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.

3.
D. F. Anderson and J. D. LaGrange, Commutative Boolean monoids, reduced rings, and the compressed zero-divisor graph, J. Pure Appl. Algebra 216 (2012), no. 7, 1626-1636. crossref(new window)

4.
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)

5.
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)

6.
M. Axtell, J. Coykendall, and J. Stickles, Zero-divisor graphs of polynomials and power series over commutative rings, Comm. Algebra 33 (2005), no. 6, 2043-2050. crossref(new window)

7.
I. Beck, Coloring of commutative rings, J. Algebra 116 (1988), no. 1, 208-226. crossref(new window)

8.
J. Coykendall, S. Sather-Wagstaff, L. Sheppardson, and S. Spiroff, On zero divisor graphs, in C. Francisco, et al. (Eds.), Progress in Commutative Algebra II: Closures, Finiteness and Factorization, de Gruyter, Berlin, 2012.

9.
F. DeMeyer and L. DeMeyer, Zero divisor graphs of semigroups, J. Algebra 283 (2005), no. 1, 190-198. crossref(new window)

10.
F. 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)

11.
F. DeMeyer and K. Schneider, Automorphisms and zero divisor graphs of commutative rings, Commutative rings, 25-37, Nova Sci. Publ., Hauppauge, NY, 2002.

12.
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)

13.
T. G. Lucas, The diameter of a zero divisor graph, J. Algebra 301 (2006), no. 1, 174-193. crossref(new window)

14.
S. B. Mulay, Cycles and symmetries of zero-divisors, Comm. Algebra 30 (2002), no. 7, 3533-3558. crossref(new window)

15.
S. Park and J. Han, The group of graph automorphisms over a matrix ring, J. Korean Math. Soc. 48 (2011), no. 2, 301-309. crossref(new window)

16.
S. P. Redmond, The zero-divisor graph of a noncommutative ring, Int. J. Commut. Rings 1 (2002), no. 4, 203-211.

17.
S. Spiroff and C. Wickham, A zero divisor graph determined by equivalence classes of zero divisors, Comm. Algebra 39 (2011), no. 7, 2338-2348. crossref(new window)