Table of Contents
Algebra
Volume 2014, Article ID 146873, 6 pages
http://dx.doi.org/10.1155/2014/146873
Research Article

Zero Divisor Graph for the Ring of Eisenstein Integers Modulo

Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan

Received 26 March 2014; Revised 19 October 2014; Accepted 24 October 2014; Published 15 December 2014

Academic Editor: Ricardo L. Soto Montero

Copyright © 2014 Osama Alkam and Emad Abu Osba. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. O. Alkam and E. Abu Osba, “On Eisenstein integers modulo n,” International Mathematical Forum, vol. 5, no. 21–24, pp. 1075–1082, 2010. View at Google Scholar · View at MathSciNet
  2. I. Beck, “Coloring of commutative rings,” Journal of Algebra, vol. 116, no. 1, pp. 208–226, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  3. D. D. Anderson and M. Naseer, “Beck's coloring of a commutative ring,” Journal of Algebra, vol. 159, no. 2, pp. 500–514, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  4. D. F. Anderson and P. S. Livingston, “The zero-divisor graph of a commutative ring,” Journal of Algebra, vol. 217, no. 2, pp. 434–447, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  5. S. Akbari and A. Mohammadian, “On the zero-divisor graph of a commutative ring,” Journal of Algebra, vol. 274, no. 2, pp. 847–855, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  6. S. Akbari and A. Mohammadian, “On zero-divisor graphs of finite rings,” Journal of Algebra, vol. 314, no. 1, pp. 168–184, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. S. Akbari, H. R. Maimani, and S. Yassemi, “When a zero-divisor graph is planar or a complete r-partite graph,” Journal of Algebra, vol. 270, no. 1, pp. 169–180, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. E. Abu Osba, S. Al-Addasi, and N. Abu Jaradeh, “Zero divisor graph for the ring of Gaussian integers modulo n,” Communications in Algebra, vol. 36, no. 10, pp. 3865–3877, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. S. B. Mulay, “Cycles and symmetries of zero-divisors,” Communications in Algebra, vol. 30, no. 7, pp. 3533–3558, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  10. R. Diestel, Graph Theory, Springer, Berlin , Germany, 2005. View at MathSciNet
  11. D. F. Anderson, A. Frazier, A. Lauve, and P. S. Livingston, “The zero-divisor graph of a commutative ring: II,” in Ideal Theoretic Methods in Commutative Algebra (Columbia, MO, 1999), vol. 220 of Lecture Notes in Pure and Appl. Math., pp. 61–72, Marcel Dekker, New York, NY, USA, 2001. View at Google Scholar
  12. M. Axtell, J. Stickles, and J. Warfel, “Zero-divisor graphs of direct products of commutative rings,” Houston Journal of Mathematics, vol. 32, no. 4, pp. 985–994, 2006. View at Google Scholar · View at MathSciNet · View at Scopus
  13. E. A. Osba and H. Al-Ezeh, “Eulerian zero-divisor graphs,” Ars Combinatoria, vol. 108, pp. 305–311, 2013. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus