대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제61권2호
  • /
  • Pages.301-315
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  • 2024
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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ON THE GENERALIZED PRINCIPALLY INJECTIVE MODULES

  • 투고 : 2022.11.17
  • 심사 : 2023.11.27
  • 발행 : 2024.03.31
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초록

Some results are generalized from principally injective rings to principally injective modules. Moreover, it is proved that the results are valid to some other extended injectivity conditions which may be defined over modules. The influence of such injectivity conditions are studied for both the trace and the reject submodules of some modules over commutative rings. Finally, a correction is given to a paper related to the subject.

키워드

과제정보

This work was financially supported by a grant from Payame Noor University of I. R. of Iran.

참고문헌

  1. A. M. Aghdam and A. Najafizadeh, Square submodule of a module, Mediterr. J. Math. 7 (2010), no. 2, 195-207. https://doi.org/10.1007/s00009-010-0041-4
  2. I. Amin, M. Yousif, and N. Zeyada, Soc-injective rings and modules, Comm. Algebra 33 (2005), no. 11, 4229-4250. https://doi.org/10.1080/00927870500279001
  3. H. Ansari-Toroghy, M-injectivity and asymptotic behaviour, Bull. Korean Math. Soc. 39 (2002), no. 2, 251-258. https://doi.org/10.4134/BKMS.2002.39.2.251
  4. S. Chotchaisthit, When is a quasi-p-injective module continuous?, Southeast Asian Bull. Math. 26 (2002), no. 3, 391-394. https://doi.org/10.1007/s10012-002-0391-3
  5. L. Fuchs and S. B. Lee, Weak-injectivity and almost perfect domains, J. Algebra 321 (2009), no. 1, 18-27. https://doi.org/10.1016/j.jalgebra.2008.08.033
  6. L. Fuchs and S. B. Lee, On weak-injective modules over integral domains, J. Algebra 323 (2010), no. 7, 1872-1878. https://doi.org/10.1016/j.jalgebra.2010.02.005
  7. Z. Gao and F. Wang, Weak injective and weak flat modules, Comm. Algebra 43 (2015), no. 9, 3857-3868. https://doi.org/10.1080/00927872.2014.924128
  8. K. R. Goodearl and R. B. Warfield Jr., An Introduction to Noncommutative Notherian Rings, Cambridge Univ. Press, Cambridge, 2004. https://doi.org/10.1017/CBO9780511841699
  9. C. Y. Hong, J. Y. Kim, and N. K. Kim, On von Neumann regular rings, Comm. Algebra 28 (2000), no. 2, 791-801. https://doi.org/10.1080/00927870008826860
  10. H. Khabazian, S. Safaeeyan, and M. R. Vedadi, Strongly duo modules and rings, Comm. Algebra 38 (2010), no. 8, 2832-2842. https://doi.org/10.1080/00927870903085245
  11. W. Li, J. Guan, and B. Ouyang, Strongly F P-injective modules, Comm. Algebra 45 (2017), no. 9, 3816-3824. https://doi.org/10.1080/00927872.2016.1247452
  12. W. K. Nicholson, J. K. Park, and M. F. Yousif, Principally quasi-injective modules, Comm. Algebra 27 (1999), no. 4, 1683-1693. https://doi.org/10.1080/00927879908826521
  13. W. K. Nicholson and M. F. Yousif, Principally injective rings, J. Algebra 174 (1995), no. 1, 77-93. https://doi.org/10.1006/jabr.1995.1117
  14. G. Puninskii and R. Wisbauer, Σ-injective modules over left duo and left distributive rings, J. Pure Appl. Algebra 113 (1996), no. 1, 55-66. https://doi.org/10.1016/0022-4049(95)00153-0
  15. N. V. Sanh, K. P. Shum, S. Dhompongsa, and S. Wongwai, On quasi-principally injective modules, Algebra Colloq. 6 (1999), no. 3, 269-276.
  16. B. T. Stenstrom, Rings of quotients, Die Grundlehren der mathematischen Wissenschaften, Band 217, Springer, New York, 1975.
  17. R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach Science Publishers, 1991.
  18. G. Xiao and W. Tong, On injectivity and P-injectivity, Bull. Korean Math. Soc. 43 (2006), no. 2, 299-307. https://doi.org/10.4134/BKMS.2006.43.2.299
  19. R. Yue Chi Ming, On (von Neumann) regular rings, Proc. Edinburgh Math. Soc. (2) 19 (1974/75), 89-91. https://doi.org/10.1017/S0013091500015418
  20. R. Yue Chi Ming, On simple P-injective modules, Math. Japon. 19 (1974), no. 3, 173-176.
  21. R. Yue Chi Ming, On injectivity and p-injectivity. IV, Bull. Korean Math. Soc. 40 (2003), no. 2, 223-234. https://doi.org/10.4134/BKMS.2003.40.2.223