Table of Contents Author Guidelines Submit a Manuscript
International Journal of Mathematics and Mathematical Sciences
Volume 2008, Article ID 469725, 7 pages
http://dx.doi.org/10.1155/2008/469725
Research Article

AGQP-Injective Modules

1Department of Mathematics, Jiaxing University, Jiaxing, Zhejiang 314001, China
2Department of Mathematics, Southeast University, Nanjing 210096, China

Received 23 December 2007; Revised 20 April 2008; Accepted 20 June 2008

Academic Editor: Robert Lowen

Copyright © 2008 Zhanmin Zhu and Xiaoxiang Zhang. 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. W. K. Nicholson and M. F. Yousif, β€œPrincipally injective rings,” Journal of Algebra, vol. 174, no. 1, pp. 77–93, 1995. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  2. S. B. Nam, N. K. Kim, and J. Y. Kim, β€œOn simple GP-injective modules,” Communications in Algebra, vol. 23, no. 14, pp. 5437–5444, 1995. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  3. N. V. Sanh, K. P. Shum, S. Dhompongsa, and S. Wongwai, β€œOn quasi-principally injective modules,” Algebra Colloquium, vol. 6, no. 3, pp. 269–276, 1999. View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  4. R. Yue Chi Ming, β€œOn injectivity and p-injectivity,” Journal of Mathematics of Kyoto University, vol. 27, no. 3, pp. 439–452, 1987. View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  5. J. Chen, Y. Zhou, and Z. Zhu, β€œGP-injective rings need not be P-injective,” Communications in Algebra, vol. 33, no. 7, pp. 2395–2402, 2005. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  6. S. S. Page and Y. Zhou, β€œGeneralizations of principally injective rings,” Journal of Algebra, vol. 206, no. 2, pp. 706–721, 1998. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  7. Z. Zhu, β€œOn general quasi-principally injective modules,” Southeast Asian Bulletin of Mathematics, vol. 30, no. 2, pp. 391–397, 2006. View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  8. W. K. Nicholson, J. K. Park, and M. F. Yousif, β€œPrincipally quasi-injective modules,” Communications in Algebra, vol. 27, no. 4, pp. 1683–1693, 1999. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  9. N. V. Dung, D. V. Huynh, P. F. Smith, and R. Wisbauer, Extending Modules, vol. 313 of Pitman Research Notes in Mathematics Series, Longman Scientific & Technical, Harlow, UK, 1994. View at Zentralblatt MATH Β· View at MathSciNet
  10. M. F. Yousif and Y. Zhou, β€œRings for which certain elements have the principal extension property,” Algebra Colloquium, vol. 10, no. 4, pp. 501–512, 2003. View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  11. S. K. Jain and S. R. López-Permouth, β€œRings whose cyclics are essentially embeddable in projective modules,” Journal of Algebra, vol. 128, no. 1, pp. 257–269, 1990. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  12. Y. Zhou, β€œRings in which certain right ideals are direct summands of annihilators,” Journal of the Australian Mathematical Society, vol. 73, no. 3, pp. 335–346, 2002. View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  13. J. Chen and N. Ding, β€œOn regularity of rings,” Algebra Colloquium, vol. 8, no. 3, pp. 267–274, 2001. View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  14. R. Wisbauer, Foundations of Module and Ring Theory, vol. 3 of Algebra, Logic and Applications, Gordon and Breach Science, Philadelphia, Pa, USA, German edition, 1991. View at Zentralblatt MATH Β· View at MathSciNet
  15. R. Wisbauer, M. F. Yousif, and Y. Zhou, β€œIkeda-Nakayama modules,” Contributions to Algebra and Geometry, vol. 43, no. 1, pp. 111–119, 2002. View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  16. Z. Zhu, Z. Xia, and Z. Tan, β€œGeneralizations of principally quasi-injective modules and quasiprincipally injective modules,” International Journal of Mathematics and Mathematical Sciences, vol. 2005, no. 12, pp. 1853–1860, 2005. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet