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SOME RESULTS ON GQP-INJECTIVE MODULES

Year 2009, Volume: 5 Issue: 5, 1 - 6, 01.06.2009

Abstract

Let R be a ring. In this note we study some properties of GQP-injective R−modules, some results on GP-injective rings and QP-injective modules are extended to these modules. Some new properties of GP-injective rings are obtained.

References

  • T. Albu and R. Wisbauer, Kasch modules, Advances in Ring Theory, S. K. Jain and S. T. Rizvi (eds.), Birkh¨auser, 1997, 1-16.
  • J. L. Chen and N. Q. Ding, On general principally injective rings, Comm. Algebra, 27(5) (1999), 2097-2116.
  • J. L. Chen, Y. Q. Zhou and Z. M. Zhu, GP-injective rings need not be P- injective, Comm. Algebra, 33(7) (2005), 2395-2402.
  • W. K. Nicholson and M. F. Yousif, Principally injective rings, J. Algebra, 174 (1995), 77-93.
  • W. K. Nicholson, J. K. Park and M. F. Yousif, Principally quasi-injective modules, Comm. Algebra, 27(4) (1999), 1683-1693.
  • N. V. Sanh, K. P. Shum, S. Dhompongsa and S. Wongwai, On quasi-principally injective modules, Algebra Colloq., 6(3)(1999), 269-276.
  • N. V. Sanh and K. P. Shum, Endomorphism rings of quasi-principally injective modules, Comm. Algebra, 29(4) (2001), 1437-1443.
  • M. F. Yousif and Y. Q. Zhou, Rings for which certain elements have the prin- cipal extension property, Algebra Colloq., 10(4) (2003), 501-512.
  • Y. Q. Zhou, Rings in which certain right ideals are direct summands of anni- hilators, J. Aust. Math. Soc., 73(3) (2002), 335-346.
  • Z. M. Zhu, On general quasi-principally injective modules, Southeast Asian Bull. Math., 30(2) (2006), 391-397.
  • Z. M. Zhu and Z. S. Tan, A note on quasi P-injective modules, Sci. Math. Jpn., (3) (2005), 461-464.
  • Z. M. Zhu, Z. S. Xia and Z. S. Tan, Generalizations of principally quasi- injective modules and quasiprincipally injective modules, Int. J. Math. Math. Sci., (12) (2005), 1853-1860. Zhanmin Zhu
  • Department of Math., Jiaxing University, Jiaxing, Zhejiang Province, , China. e-mail: zhanmin zhu@hotmail.com
Year 2009, Volume: 5 Issue: 5, 1 - 6, 01.06.2009

Abstract

References

  • T. Albu and R. Wisbauer, Kasch modules, Advances in Ring Theory, S. K. Jain and S. T. Rizvi (eds.), Birkh¨auser, 1997, 1-16.
  • J. L. Chen and N. Q. Ding, On general principally injective rings, Comm. Algebra, 27(5) (1999), 2097-2116.
  • J. L. Chen, Y. Q. Zhou and Z. M. Zhu, GP-injective rings need not be P- injective, Comm. Algebra, 33(7) (2005), 2395-2402.
  • W. K. Nicholson and M. F. Yousif, Principally injective rings, J. Algebra, 174 (1995), 77-93.
  • W. K. Nicholson, J. K. Park and M. F. Yousif, Principally quasi-injective modules, Comm. Algebra, 27(4) (1999), 1683-1693.
  • N. V. Sanh, K. P. Shum, S. Dhompongsa and S. Wongwai, On quasi-principally injective modules, Algebra Colloq., 6(3)(1999), 269-276.
  • N. V. Sanh and K. P. Shum, Endomorphism rings of quasi-principally injective modules, Comm. Algebra, 29(4) (2001), 1437-1443.
  • M. F. Yousif and Y. Q. Zhou, Rings for which certain elements have the prin- cipal extension property, Algebra Colloq., 10(4) (2003), 501-512.
  • Y. Q. Zhou, Rings in which certain right ideals are direct summands of anni- hilators, J. Aust. Math. Soc., 73(3) (2002), 335-346.
  • Z. M. Zhu, On general quasi-principally injective modules, Southeast Asian Bull. Math., 30(2) (2006), 391-397.
  • Z. M. Zhu and Z. S. Tan, A note on quasi P-injective modules, Sci. Math. Jpn., (3) (2005), 461-464.
  • Z. M. Zhu, Z. S. Xia and Z. S. Tan, Generalizations of principally quasi- injective modules and quasiprincipally injective modules, Int. J. Math. Math. Sci., (12) (2005), 1853-1860. Zhanmin Zhu
  • Department of Math., Jiaxing University, Jiaxing, Zhejiang Province, , China. e-mail: zhanmin zhu@hotmail.com
There are 13 citations in total.

Details

Other ID JA56PG94RH
Journal Section Articles
Authors

Zhanmin Zhu This is me

Publication Date June 1, 2009
Published in Issue Year 2009 Volume: 5 Issue: 5

Cite

APA Zhu, Z. (2009). SOME RESULTS ON GQP-INJECTIVE MODULES. International Electronic Journal of Algebra, 5(5), 1-6.
AMA Zhu Z. SOME RESULTS ON GQP-INJECTIVE MODULES. IEJA. June 2009;5(5):1-6.
Chicago Zhu, Zhanmin. “SOME RESULTS ON GQP-INJECTIVE MODULES”. International Electronic Journal of Algebra 5, no. 5 (June 2009): 1-6.
EndNote Zhu Z (June 1, 2009) SOME RESULTS ON GQP-INJECTIVE MODULES. International Electronic Journal of Algebra 5 5 1–6.
IEEE Z. Zhu, “SOME RESULTS ON GQP-INJECTIVE MODULES”, IEJA, vol. 5, no. 5, pp. 1–6, 2009.
ISNAD Zhu, Zhanmin. “SOME RESULTS ON GQP-INJECTIVE MODULES”. International Electronic Journal of Algebra 5/5 (June 2009), 1-6.
JAMA Zhu Z. SOME RESULTS ON GQP-INJECTIVE MODULES. IEJA. 2009;5:1–6.
MLA Zhu, Zhanmin. “SOME RESULTS ON GQP-INJECTIVE MODULES”. International Electronic Journal of Algebra, vol. 5, no. 5, 2009, pp. 1-6.
Vancouver Zhu Z. SOME RESULTS ON GQP-INJECTIVE MODULES. IEJA. 2009;5(5):1-6.