Table of Contents
Algebra
Volume 2015 (2015), Article ID 595274, 4 pages
http://dx.doi.org/10.1155/2015/595274
Research Article

Generalized Malcev-Neumann Series Modules with the Beachy-Blair Condition

1Department of Mathematics and Statistics, Faculty of Science, Taif University, P.O. Box 888, Al-Hawiyah, Taif 21974, Saudi Arabia
2Mathematics Department, Faculty of Science, Al-Azhar University, P.O. Box 11884, Nasr City, Cairo, Egypt

Received 9 January 2015; Revised 9 March 2015; Accepted 10 March 2015

Academic Editor: Andrei V. Kelarev

Copyright © 2015 Mohamed A. Farahat. 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. A. Malcev, “On embedding of group algebras in a division algebra,” Doklady Akademii Nauk, vol. 60, pp. 1499–1501, 1948 (Russian). View at Google Scholar
  2. B. H. Neumann, “On ordered division rings,” Transactions of the American Mathematical Society, vol. 66, pp. 202–252, 1949. View at Publisher · View at Google Scholar · View at MathSciNet
  3. A. V. Kelarev, Ring Constructions and Applications, World Scientific, River Edge, NJ, USA, 2002. View at MathSciNet
  4. C. Faith, “Annihilator ideals, associated primes and Kasch-McCoy commutative rings,” Communications in Algebra, vol. 19, no. 7, pp. 1867–1892, 1991. View at Publisher · View at Google Scholar · View at MathSciNet
  5. J. M. Zelmanowitz, “The finite intersection property on annihilator right ideals,” Proceedings of the American Mathematical Society, vol. 57, no. 2, pp. 213–216, 1976. View at Publisher · View at Google Scholar · View at MathSciNet
  6. C. Zhang and J. Chen, “Zip modules,” Northeastern Mathematical Journal, vol. 24, pp. 240–256, 2008. View at Google Scholar
  7. E. Rodríguez-Jorge, “Rings with the Beachy-Blair condition,” Journal of Algebra and Its Applications, vol. 11, no. 1, Article ID 1250006, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  8. L. Ouyang, J. Liu, and Y. Xiang, “Modules with the Beachy-Blair condition,” Communications in Algebra, vol. 42, no. 2, pp. 853–871, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. R. M. Salem, A. M. Hassanein, and M. A. Farahat, “Mal'cev-Neumann series over zip and weak zip rings,” Asian-European Journal of Mathematics, vol. 5, no. 4, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. G. Renault, “Anneaux reduits non commutatifs,” Journal de Mathématiques Pures et Appliquées, vol. 46, pp. 203–214, 1967. View at Google Scholar
  11. T.-K. Lee and Y. Zhou, “Reduced modules,” in Rings, Modules, Algebras and Abelian Groups, vol. 236 of Lecture Notes in Pure and Applied Mathematics, pp. 365–377, Marcel Dekker, New York, NY, USA, 2004. View at Google Scholar · View at MathSciNet