150
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Implements of Graph Blow-Up in Co-Maximal Ideal Graphs

, , &
Pages 2476-2483 | Received 29 Mar 2012, Published online: 01 Feb 2014

REFERENCES

  • Anderson , D. F. , Axtell , M. C. , Stickles , J. A. ( 2011 ). Zero-divisor graphs in commutative rings . In: Fontana , M. , Kabbaj , S. E. , Olberding , B. , Swanson , I. eds. Commutative Algebra, Noetherian and Non-Noetherian Perspectives . Springer Science + Business Media , pp. 434 – 447 .
  • Anderson , D. F. , Livingston , P. S. ( 1999 ). The zero-divisor graph of a commutative ring . J. Algebra 217 : 434 – 447 .
  • Hell , P. , Nešetřil , J. ( 2004 ). Graphs and Homomorphisms . Oxford Lecture Series in Mathematics and Its Applications . Oxford : Oxford University Press .
  • Komlós , J. , Sárközy , G. N. , Szemerédi , E. ( 1997 ). Blow-up lemma . Combinitorica 17 ( 1 ): 109 – 123 .
  • LaGrange , J. D. ( 2007 ). Complemented zero-divisor graphs and Boolean rings . J. Algebra 315 : 600 – 611 .
  • Lu , D. C. , Wu , T. S. ( 2007 ). The zero-divisor graphs which are uniquely determined by neighborhoods . Comm. Algebra 35 ( 12 ): 3855 – 3864 .
  • Maimani , H. R. , Salimi , M. , Sattari , A. , Yassemi , S. ( 2008 ). Comaximal graph of commutative rings . J. Algebra 319 ( 4 ): 1801 – 1808 .
  • Moconja , S. M. , Petrović , Z. Z. ( 2011 ). On the structure of comaximal graphs of commutative rings with identity . Bull. Aust. Math. Soc. 83 : 11 – 21 .
  • Nikiforov , V. ( 2008 ). Graphs with many copies of a given subgraph . Electron. J. Combin. 15 ( 1 ): #N6 .
  • Sharma , P. K. , Bhatwadekar , S. M. ( 1995 ). A note on graphical representation of rings . J. Algebra 176 : 124 – 127 .
  • Sharp , R. Y. ( 2001 ). Steps in Commutative Algebra, , 2nd ed. Cambridge University Press. London Mathematical Society Student Texts , Vol. 51 , London .
  • Wang , H. J. ( 2008 ). Graphs associated to co-maximal ideals of commutative rings . J. Algebra 320 ( 7 ): 2917 – 2933 .
  • West , D. B. ( 2004 ). Introduction to Graph Theory. , 2nd ed. Pearson Education Asia Limited and China Machine Press .
  • Wu , T. S. , Chen , L. ( 2009 ). Simple graphs and commutative zero-divisor semigroups . Algebra Colloq. 16 ( 2 ): 211 – 218 .
  • Wu , T. S. , Ye , M. , Lu , D. C. , Yu , H. Y. On ring graphs related to co-maximal ideals . ISRN Combinatorics (accepted) .
  • Ye , M. , Wu , T. S. ( 2012 ). Co-maximal ideal graphs of commutative rings . Journal of Algebra and Its Applications 16 ( 6 ): 1250114 (14 pages) .
  • Communicated by I. Swanson.

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.