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The Scientific World Journal
Volume 2013 (2013), Article ID 650702, 8 pages
http://dx.doi.org/10.1155/2013/650702
Research Article

Reversible Rings with Involutions and Some Minimalities

Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received 12 September 2013; Accepted 24 November 2013

Academic Editors: A. Badawi and Y. Lee

Copyright © 2013 W. M. Fakieh and S. K. Nauman. 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. P. M. Cohn, “Reversible rings,” Bulletin of the London Mathematical Society, vol. 31, no. 6, pp. 641–648, 1999. View at Google Scholar · View at Scopus
  2. D. D. Anderson and V. Camillo, “Semigroups and rings whose zero products commute,” Communications in Algebra, vol. 27, no. 6, pp. 2847–2852, 1999. View at Google Scholar · View at Scopus
  3. M. Başer, C. Y. Hong, and T. K. Kwak, “On extended reversible rings,” Algebra Colloquium, vol. 16, no. 1, pp. 37–48, 2009. View at Google Scholar · View at Scopus
  4. M. Baser and T. K. Kwak, “On strong reversible rings and their extensions,” Korean Journal of Mathematics, vol. 18, no. 2, pp. 119–132, 2010. View at Google Scholar
  5. S. Feigelstock, Additive Groups of Rings, vol. 11, Pitman Advanced Publishing Program, 1983.
  6. J. Lambek, “On the representation of modules by sheaves of factor modules,” Canadian Mathematical Bulletin, vol. 14, pp. 359–368, 1971. View at Publisher · View at Google Scholar
  7. V. Camillo and P. P. Nielsen, “McCoy rings and zero-divisors,” Journal of Pure and Applied Algebra, vol. 212, no. 3, pp. 599–615, 2008. View at Publisher · View at Google Scholar · View at Scopus
  8. G. Marks, “Reversible and symmetric rings,” Journal of Pure and Applied Algebra, vol. 174, no. 3, pp. 311–318, 2002. View at Publisher · View at Google Scholar · View at Scopus
  9. S. K. Nauman and B. H. Shafee, “A note on right symmetric rings,” submitted.
  10. H. E. Bell, “Near-rings, in which every element is a power of itself,” Bulletin of the Australian Mathematical Society, vol. 2, no. 3, pp. 363–368, 1970. View at Publisher · View at Google Scholar
  11. G. Marks, “A taxonomy of 2-primal rings,” Journal of Algebra, vol. 266, no. 2, pp. 494–520, 2003. View at Publisher · View at Google Scholar · View at Scopus
  12. C. Huh, Y. Lee, and A. Smoktunowicz, “Armendariz rings and semicommutative rings,” Communications in Algebra, vol. 30, no. 2, pp. 751–761, 2002. View at Publisher · View at Google Scholar · View at Scopus
  13. F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Graduate Text in Mathematics, Springer, New York, NY, USA, 2nd edition, 1992.
  14. T. Y. Lam, A First Course in Modules and Rings, Graduate Texts in Mathematics, Springer, New York, NY, USA, 1999.
  15. U. A. Aburawash and W. M. Fakieh, “Strongly principal ideals of rings with involution,” International Journal of Algebra, vol. 2, no. 14, pp. 685–700, 2008. View at Google Scholar
  16. G. F. Birkenmeir and N. J. Groenewald, “Prime ideals in rings with involution,” Quaestiones in Mathematicae, vol. 20, no. 4, pp. 591–603, 1997. View at Publisher · View at Google Scholar
  17. M. A. Knus, A. S. Merkurjev, M. Rost, and J. P. Tignol, The Book of Involutions, vol. 44 of American Mathematical Society Colloquium Publications, American Mathematical Society, Providence, RI, USA, 1988.
  18. D. I. C. Mendes, “A note on involution rings,” Miskolc Mathematical Notes, vol. 10, no. 2, pp. 155–162, 2009. View at Google Scholar
  19. L. Oukhtite and S. Salhi, “σ-prime rings with a special kind of automorphism,” International Journal of Contemporary Mathematical Sciences, vol. 2, no. 3, pp. 127–133, 2007. View at Google Scholar
  20. N. K. Kim and Y. Lee, “Extensions of reversible rings,” Journal of Pure and Applied Algebra, vol. 185, no. 1–3, pp. 207–223, 2003. View at Publisher · View at Google Scholar · View at Scopus
  21. C. Huh, H. K. Kim, N. K. Kim, and Y. Lee, “Basic examples and extensions of symmetric rings,” Journal of Pure and Applied Algebra, vol. 202, no. 1-3, pp. 154–167, 2005. View at Publisher · View at Google Scholar · View at Scopus
  22. E. P. Armendariz, “A note on extension of Baer and P.P.-rings,” Journal of the Australian Mathematical Society, vol. 18, no. 4, pp. 470–473, 1974. View at Publisher · View at Google Scholar
  23. B. O. Kim and Y. Lee, “Minimal noncommutative reversible and reflexive rings,” Bulletin of the Korean Mathematical Society, vol. 48, no. 3, pp. 611–616, 2011. View at Publisher · View at Google Scholar