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Research Article

Ideally nil clean rings

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Pages 4788-4799 | Received 30 Jan 2021, Accepted 08 Apr 2021, Published online: 08 Jun 2021

References

  • Sheibani Abdolyousefi, M., Ashrafi, N., Chen, H. (2019). On unit nil-clean rings. Mediterr. J. Math. 16(4):100. DOI: 10.1007/s00009-019-1369-z.
  • Andrica, D., Călugăreanu, G. (2014). A nil-clean 2 × 2 matrix over the integers which is not clean. J. Algebra Appl. 13(06):1450009. DOI: 10.1142/S0219498814500091.
  • Camillo, V. P., Yu, H.-P. (1998). On rings whose prime factors are simple. Sci. Math. 1(3):293–296.
  • Chen, H., Sheibani, M. (2017). On strongly nil clean rings. Commun. Algebra 45(4):1719–1726. DOI: 10.1080/00927872.2016.1222411.
  • Danchev, P., Šter, J. (2015). Generalizing π-regular rings. Taiwanese J. Math. 19(6):1577–1592. DOI: 10.11650/tjm.19.2015.6236.
  • Diesl, A. J. (2013). Nil clean rings. J. Algebra 383:197–211. DOI: 10.1016/j.jalgebra.2013.02.020.
  • Fisher, J. W., Snider, R. L. (1974). On the von Neumann regularity of rings with regular prime factor rings. Pacific J. Math. 54(1):135–144. DOI: 10.2140/pjm.1974.54.135.
  • Yasuyuki, H., Hisao, T., Adil, Y. (1988). On rings in which every element is uniquely expressible as a sum of a nilpotent element and a certain potent element. Math. J. Okayama Univ. 30:33–40.
  • Hong, C. Y., Kim, N. K., Kwak, T. K., Lee, Y. (2000). On weak π-regularity of rings whose prime ideals are maximal. J. Pure Appl. Algebra 146(1):35–44. DOI: 10.1016/S0022-4049(98)00177-7.
  • Jeon, Y. C., Kim, N. K., Lee, Y. (2010). On fully idempotent rings. Bull. Korean Math. Soc. 47(4):715–726. DOI: 10.4134/BKMS.2010.47.4.715.
  • Karparvar, A. M., Amini, B., Amini, A., Sharif, H. (2018). Additive decomposition of ideals. J. Algebra Appl. 17(05):1850085. 17 DOI: 10.1142/S0219498818500858.
  • Khashan, H. A. (2016). NR-clean rings. Vietnam J. Math. 44(4):749–759. DOI: 10.1007/s10013-016-0197-8.
  • Lam, T. Y. (2001). A First Course in Noncommutative Rings, Volume 131 of Graduate Texts in Mathematics, 2nd ed. New York: Springer-Verlag.
  • Lam, T. Y. (2003). Exercises in classical ring theory. Problem Books in Mathematics, 2nd ed. New York: Springer-Verlag.
  • McCoy, N. H. (1939). Generalized regular rings. Bull. Amer. Math. Soc. 45(2):175–178. DOI: 10.1090/S0002-9904-1939-06933-4.
  • Nicholson, W. K. (1977). Lifting idempotents and exchange rings. Trans. Amer. Math. Soc. 229:269–278. DOI: 10.1090/S0002-9947-1977-0439876-2.
  • Masayuki, Ô. (1985). On strongly π-regular rings and periodic rings. Math. J. Okayama Univ. 27:49–52.
  • Smith, P. F. (1975/76). A note on projective modules. Proc. Roy. Soc. Edinburgh Sect. A. 75(1):23–31.
  • Smoktunowicz, A. (2002). A simple nil ring exists. Commun. Algebra 30(1):27–59. DOI: 10.1081/AGB-120006478.
  • Šter, J. (2018). On expressing matrices over Z2 as the sum of an idempotent and a nilpotent. Linear Algebra Appl. 544:339–349.
  • Xue, Y. (1985). Weakly right duo rings. Pure Appl. Math. Sci. 21(1-2):19–24.
  • Yu, H.-P. (1995). On quasi-duo rings. Glasgow Math. J. 37(1):21–31. DOI: 10.1017/S0017089500030342.

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