Acknowledgement
This work was financially supported by a grant from Payame Noor University of I. R. of Iran.
References
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- N. V. Sanh, K. P. Shum, S. Dhompongsa, and S. Wongwai, On quasi-principally injective modules, Algebra Colloq. 6 (1999), no. 3, 269-276.
- B. T. Stenstrom, Rings of quotients, Die Grundlehren der mathematischen Wissenschaften, Band 217, Springer, New York, 1975.
- R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach Science Publishers, 1991.
- 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
- 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
- R. Yue Chi Ming, On simple P-injective modules, Math. Japon. 19 (1974), no. 3, 173-176.
- 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