On Almost WJCP-Injective Rings

Section: Research Paper
Published
Mar 1, 2019
Pages
83-89

Abstract

Let R be a ring. The ring is called right almost WJCP-injective. If for any , (right non singular) there exists a left ideal of such that . In this paper, we give some characterization and properties of almost WJCP-injective rings, which are proper generalization of JCP-injective ring and almost AP-injective ring. Then, we study the regularity of the right almost WJCP-injective ring and some important results which are known for the right JCP-injective rings to be hold for the right almost WJCP-injective rings.

References

  1. Camillo, V. and Nicholoson, W.K., (2015), On rings where left principal ideal are left principal annihilators, Inter Electronic J. of Algebra. Vol. 17, pp. 199-214.
  2. Yue Chi Ming, R., (1983), On quasi frobeniusean and artinian rings, Pub. De Linstitut. Math. matique, 33(47), pp. 239-245.
  3. Yue Chi Ming, R., (1999), A note on biregular rings, Kyngpook. Math. J., Vol. 39, pp. 165-173.
  4. Zhao, Yu-e and Du Xia, (2002), Some studies on AP-injective rings", J. of Anhui Un.,Vo1. 26(1), pp. 7-11.
  5. Zhao, Yu-e and Du Xia, (2011), On almost nil-injective rings, Inter Elec. J. of Algebra, Vo1. 9, pp. 103-113.
  6. Zhao, Yu-e, (2011), On simple singular AP-injective modules, Inter. Math. froum. Vol. 6, No. 21, pp. 1037-1043.
  7. Chen, J.L. and Ding, N.Q., (1999), On general principally injective rings, Comm. Algebra, Vol. 27, pp. 2097-2116.
  8. Goodearl, K.R., (1979), Von Neumann regular rings, Pitman (London).
  9. Nicholson, W.K. and Yousif, M.F., (1995), Principally injective rings, J. Algebra, Vol. 174, pp. 77-93.
  10. Page, S.S. and Zhou, Y.Q., (1998), Generalization of principally injective rings, J. Algebra, Vol. 206, pp. 706-721.
  11. Subedi, T., (2012), On strongly regular rings and generalizations of semicommutative rings, Inter. Math. Forum, Vol. 7, No. 16, pp. 777-790.
  12. Wei, J.C., (2009), JCP-injective rings, Int. Electron. J. of Algebra, Vol. 6, pp. 1-22.
  13. Yang Xiang, (2011), Almost principally small injective rings, J. Kor. Math. Soc., Vol. 48, No. 6, pp. 1189-1201.
  14. Yue Chi Ming, R., (1976), On annihilator ideals, Math. J. Oka. Univ., Vol. 19, pp. 51-53.
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How to Cite

[1]
S. Hatem Ahmed, شیماء, R. Dawood Mahmoud, and رائدة, “On Almost WJCP-Injective Rings”, EDUSJ, vol. 28, no. 1, pp. 83–89, Mar. 2019.