Have a personal or library account? Click to login
The quasi-Zariski topology-graph on the maximal spectrum of modules over commutative rings Cover

The quasi-Zariski topology-graph on the maximal spectrum of modules over commutative rings

By: H. Ansari-Toroghy and  Sh. Habibi  
Open Access
|Dec 2018

References

  1. [1] D. F. Anderson, M. C. Axtell and J. A. Stickles, Jr., Zero-divisor graphs in commutative rings, in Commutative Algebra, Noetherian and Non-Noetherian Perspectives, eds. M. Fontana, S.-E. Kabbaj, B. Olberding and I. Swanson, Springer-Verlag, NewYork, (2010) 2345.10.1007/978-1-4419-6990-3_2
  2. [2] D. F. Anderson and A. Badawi, On the zero-divisor graph of a ring, Comm. Algebra 36 (2008) 30733092.10.1080/00927870802110888
  3. [3] D. F. Anderson and A. Badawi, The total graph of a commutative ring, J. Algebra 320 (2008) 27062719.10.1016/j.jalgebra.2008.06.028
  4. [4] D. F. Anderson and A. Badawi, The total graph of a commutative ring with-out the zero element, J. Algebra Appl. 11(4) (2012) 12500740 (18 pages).10.1142/S0219498812500740
  5. [5] D. F. Anderson and A. Badawi, The generalized total graph of a commutative ring, Journal of Algebra and Its Applications (JAA). 12 (5) (2013).10.1142/S021949881250212X
  6. [6] D. F. Anderson, P. S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra 217 (1999) 434-447.10.1006/jabr.1998.7840
  7. [7] W. Anderson, K. R. Fuller, Rings and Categories of Modules, New York-Heidelberg-Berlin, Springer-Verlag (1974).10.1007/978-1-4684-9913-1
  8. [8] H. Ansari-Toroghy, F. Farshadifar, Product and dual product of submodules, Far East J. Math. Sci 25 (3)(2007) 447-455.
  9. [9] H. Ansari-Toroghy, Sh. Habibi, The Zariski topology-graph of modules over commutative rings, Comm. Algebra 42 (2014) 3283–3296.10.1080/00927872.2013.780065
  10. [10] H. Ansari-Toroghy, Sh. Habibi, On the graph of modules over commutative rings, Rocky Mountain J. Math 46 (3) (2016) 1–19.10.1216/RMJ-2016-46-3-729
  11. [11] H. Ansari-Toroghy, S. Keyvani, On the maximal spectrum of a module and Zariski topology, Bull. Malays. Sci. Soc, 38 (1), (2015) 303-316.10.1007/s40840-014-0020-1
  12. [12] H. Ansari-Toroghy, R. Ovlyaee-Sarmazdeh, On the prime spectrum of X-injective modules, Comm. Algebra 38 (2010) 2606-2621.10.1080/00927870903036339
  13. [13] H. Ansari-Toroghy, R. Ovlyaee-Sarmazdeh, On the prime spectrum of a module and Zariski topologies, Comm. Algebra 38 (2010) 4461-4475.10.1080/00927870903386510
  14. [14] H. Ansari-Toroghy, R. Ovlyaee-Sarmazdeh, Modules for which the natural map of the maximal spectrum is surjective, Colloq. Math, 119 (2010) 217-227.10.4064/cm119-2-4
  15. [15] A. Badawi, On the annihilator graph of a commutative ring, Comm. Algebra, 42 (1)(2014) 108-121.10.1080/00927872.2012.707262
  16. [16] Z. Barati, K. Khashyarmanesh, F. Mohammadi and Kh. Nafar, On the associated graphs to a commutative ring, J. Algebra Appl. 11(2) (2012) 1250037 (17 pages).10.1142/S0219498811005610
  17. [17] I. Beck, Coloring of commutative rings, J. Algebra 116 (1988) 208-226.10.1016/0021-8693(88)90202-5
  18. [18] M. Behboodi, M. R. Haddadi, Classical Zariski topology of modules and spectral spaces I, Int. Electron. J. Algebra, 4 (2008) 104-130.
  19. [19] M. Behboodi, O. A. S. Karamzadeh and H. Koohy, Modules whose certain ideals are prime, Vietnam J. Math. 32 (2004) 303-317.
  20. [20] M. Behboodi, Z. Rakeei, The annihilating-ideal graph of commutative rings I, J. Algebra Appl 10 (2011) 727-739.10.1142/S0219498811004896
  21. [21] Z. A. EL-Bast, P. F. Smith, Multiplication modules, Comm. Algebra 16 (1988) 755-779.10.1080/00927878808823601
  22. [22] E. Y. Habeeb, On the space of maximal submodules, M.Sc. Thesis, College of Education for Girls Department of Mathematics, University of Kufa, (2009).
  23. [23] Chin-Pi. Lu, The Zariski topology on the prime spectrum of a module, Houston J. Math 25 (1999) 417-432.
  24. [24] B. H. R. Maimani, M. R. Pouranki, A. Tehranian and S. Yassemi, Graphs attached to rings revisited, Arab. J. Sci. Eng. 36 (2011) 9971011.10.1007/s13369-011-0096-y
  25. [25] R. L. McCasland, M. E. Moor, Prime submodules. Comm. Algebra 20 (1992) 1803-1817.10.1080/00927879208824432
  26. [26] R. L. McCasland, M. E. Moore, P. F. Smith, On the spectrum of a module over a commutative ring, Comm. Algebra 25 (1997) 79-103.10.1080/00927879708825840
  27. [27] R. L. McCasland, P. F. Smith, Prime submodules Noetherian modules, Rocky Mountain J. Math 23 (1993) 1041-1062.10.1216/rmjm/1181072540
  28. [28] D. Reinard, Graph Theory, Grad, Texts in Math, Springer, NJ (2005).
  29. [29] H. A. Tavallaee, R. Varmazyar, Semi-radicals of submodules in modules, IUST International Journal of Engineering Science, 19.
DOI: https://doi.org/10.2478/auom-2018-0032 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 41 - 56
Submitted on: Nov 30, 2013
Accepted on: Nov 27, 2017
Published on: Dec 31, 2018
Published by: Ovidius University of Constanta
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2018 H. Ansari-Toroghy, Sh. Habibi, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.