References
- M. Altun-Ozarslan, Y. Ibrahim, A. C. Ozcan and M. Yousif, C4- and D4- modules via perspective direct summands, Comm. Algebra, 46(10)(2018), 4480-4497. https://doi.org/10.1080/00927872.2018.1448838
- F. W. Anderson and K. R. Fuller, Rings and categories of modules, Graduate Texts in Mathematics, vol. 13, Springer-Verlag, New York, 1974.
- E. Buyukas. ik, O. Demir and M. Diril, On simple-direct modules, Comm. Algebra, 49(2)(2021), 864-876. https://doi.org/10.1080/00927872.2020.1821207
- V. Camillo, Y. Ibrahim, M. Yousif and Y. Zhou, Simple-direct-injective modules, J. Algebra, 420(2014), 39-53. https://doi.org/10.1016/j.jalgebra.2014.07.033
- A. J. Diesl, S. J. Dittmer and P. P. Nielsen, Idempotent lifting and ring extensions, J. Algebra Appl., 15(6)(2016), 1650112 (16 pages).
- J. L. Garcia, Properties of direct summands of modules, Comm. Algebra, 17(1)(1989), 73-92. https://doi.org/10.1080/00927878908823714
- K. R. Goodearl and R. B. Warfield, Jr., An introduction to noncommutative Noetherian rings, London Math. Soc. Student Texts 16, Cambridge: Cambridge University Press, 1989.
- Y. Ibrahim, M. T. Kos.an, T. C. Quynh and M. Yousif, Simple-direct-projective modules, Comm. Algebra, 44(12)(2016), 5163-5178. https://doi.org/10.1080/00927872.2016.1147574
- D. Keskin Tutuncu, N. Orhan Ertas and R. Tribak, On dual Rickart modules and weak dual Rickart modules, Algebra Discrete Math., 25(2)(2018), 200-214.
- T. Y. Lam, Lectures on modules and rings, Graduate Texts in Mathematics, vol. 189, Springer-Verlag, New York, 1999.
- G. Lee, S. T. Rizvi and C. S. Roman, Dual Rickart modules, Comm. Algebra, 39(11)(2011), 4036-4058. https://doi.org/10.1080/00927872.2010.515639
- R. Mazurek, P. P. Nielsen and M. Ziembowski, Commuting idempotents, square-free modules, and the exchange property, J. Algebra, 444(2015), 52-80. https://doi.org/10.1016/j.jalgebra.2015.07.015
- W. K. Nicholson and M. Yousif, Quasi-Frobenius rings, Cambridge Tracts in Mathematics, vol. 158, Cambridge University Press, Cambridge, 2003.
- D. W. Sharpe and P. V'amos, Injective modules, Cambridge University Press, London-New York, 1972.
- A. Tuganbaev, Rings close to regular, Mathematics and Its Applications, vol. 545, Kluwer Academic Publishers, Dordrecht-Boston-London, 2002.
- R. B. Warfield, Jr., A Krull-Schmidt theorem for infinite sums of modules, Proc. Amer. Math. Soc., 22(2)(1969), 460-465. https://doi.org/10.1090/S0002-9939-1969-0242886-2