134
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Classifying annihilating-ideal graphs of commutative artinian rings

, &
Pages 4131-4147 | Received 09 Sep 2016, Published online: 08 Mar 2018

References

  • Aalipour, G., Akbari, S., Behboodi, M., Nikandish, R., Nikmehr, M. J., Shaveisi, F. (2014). The classification of the annihilating-ideal graphs of commutative rings. Algebra Colloq. 21(2):249–256.
  • Akbari, S., Maimani, H. R., Yassemi, S. (2003). When a zero-divisor graph is planar or a complete r-partite graph. J. Algebra 270(1):169–180.
  • Akbari, S., Mohammadian, A. (2004). On the zero-divisor graph of a commutative ring. J. Algebra 274(2):847–855.
  • Akbari, S., Mohammadian, A. (2006). Zero-divisor graphs of non-commutative rings. J. Algebra 296(2):462–479.
  • Akbari, S., Mohammadian, A. (2007). On zero-divisor graphs of finite rings. J. Algebra 314(1):168–184.
  • Anderson, D. F., Livingston, P. S. (1999). The zero-divisor graph of a commutative ring. J. Algebra 217(2):434–447.
  • Anderson, D. F., Mulay, S. B. (2007). On the diameter and girth of a zero-divisor graph. J. Pure Appl. Algebra 210(2):543–550.
  • Atiyah, M. F., Macdonald, I. G. (1969). Introduction to Commutative Algebra. Reading, Mass., London/Ont.: Addison-Wesley Publishing Co./Don Mills.
  • Beck, I. (1988). Coloring of commutative rings. J. Algebra 116(1):208–226.
  • Behboodi, M., Rakeei, Z. (2011). The annihilating-ideal graph of commutative rings I. J. Algebra Appl. 10(4):727–739.
  • Behboodi, M., Rakeei, Z. (2011). The annihilating-ideal graph of commutative rings II. J. Algebra Appl. 10(4): 741–753.
  • Chiang-Hsieh, H.-J., Smith, N. O., Wang, H.-J. (2010). Commutative rings with toroidal zero-divisor graphs. Houston J. Math. 36(1):1–31.
  • Coykendall, J., Sather-Wagstaff, S., Sheppardson, L., Spiroff, S. (2012). On zero divisor graphs. In: Progress in Commutative Algebra 2. Berlin: Walter de Gruyter, pp. 241–299.
  • DeMeyer, F., DeMeyer, L. (2005). Zero divisor graphs of semigroups. J. Algebra 283(1):190–198.
  • Harada, M. (1982). Self mini-injective rings. Osaka J. Math. 19(3):587–597.
  • Hungerford, T. W. (1968). On the structure of principal ideal rings. Pacific J. Math. 25:543–547.
  • LaGrange, J. D. (2008). On realizing zero-divisor graphs. Comm. Algebra 36(12):4509–4520.
  • LaGrange, J. D. (2016). Annihilators in zero-divisor graphs of semilattices and reduced commutative semigroups. J. Pure Appl. Algebra 220(8):2955–2968.
  • Mulay, S. B. (2002). Cycles and symmetries of zero-divisors. Comm. Algebra 30(7):3533–3558.
  • Nicholson, W. K., Yousif, M. F. (1995). Principally injective rings. J. Algebra 174(1):77–93.
  • Nicholson, W. K., Yousif, M. F. (1997). Mininjective rings. J. Algebra 187(2):548–578.
  • Redmond, S. P. (2007). On zero-divisor graphs of small finite commutative rings. Discrete Math. 307(9–10): 1155–1166.
  • Smith, N. O. (2006). Planar zero-divisor graphs. In: Focus on Commutative Rings Research. New York: Nova Sci. Publ., pp. 177–186.
  • Spiroff, S., Wickham, C. (2011). A zero divisor graph determined by equivalence classes of zero divisors. Comm. Algebra 39(7):2338–2348.
  • Yao, Y. (2008). Infinite rings with planar zero-divisor graphs. Comm. Algebra 36(11):4068–4077.
  • Yu, H., Wu, T., Gu, W. (2015). Artinian local rings whose annihilating-ideal graphs are star graphs. Algebra Colloq. 22(1):73–82.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.