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Research Articles

On rings determined by their idempotents and units

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Pages 2820-2829 | Received 24 Oct 2021, Accepted 27 Nov 2022, Published online: 03 Feb 2023

References

  • Anderson, F. W., Fuller, K. R. (1974). Rings and Categories of Modules. New York: Springer-Verlag.
  • Azarpanah, F. (2002). When is C(X) a clean ring? Acta Math. Hungar. 94(1–2):53–58. DOI: 10.1023/A:101.5654520481
  • Cǎlugǎreanu, G. (2018). A new class of semiprime rings. Houston J. Math. 44:21–30.
  • Canfell, M. J. (1970). Uniqueness of generators of principal ideals in rings of continuous functions. Proc. Amer. Math. Soc. 26:571–573. DOI: 10.1090/S0002-9939-1970-0288109-8.
  • Engelking, R. (1977). General Topology. Warszawa: PWN Polish Scientific Publishers.
  • Goodearl, K. R. (1979). Von Neumann Regular Rings. Boston, London: Pitman (Advanced Publishing Program).
  • Farshad, N., SafariSabet, S. A., Moussavi A. (2021). Amalgamated Rings with clean-type properties. Hacet. J. Math. Stat. 50(5):1358–1370. DOI: 10.15672/hujms.676342..
  • Gerasimov, V. N., Sakhaev, I. I. (1984). A counterexample to two conjectures on projective and flat modules. Siberian Math. J. 25(6):855–859. DOI: 10.1007/BF00968939.
  • Kaplansky, I. (1949). Elementary divisors and modules. Trans. Amer. Math. Soc. 66:464–491. DOI: 10.1090/S0002-9947-1949-0031470-3.
  • Koşan, M. T., Quynh, T. C., Sahinkaya, S. (2017). On rings with associated elements. Commun. Algebra. 45(7): 2747–2756. DOI: 10.1080/00927872.2016.1175595.
  • Marks, G. (2006). A criterion for unit-regularity. Acta Math. Hungar. 111(4):311–312. DOI: 10.1007/s10474-006-0055-3.
  • McGovern, W. Wm. (2003). Clean semiprime f-rings with bounded inversion. Commun. Algebra. 31(7):3295–3304. DOI: 10.1081/AGB-120022226.
  • Nicholson, W. K. (1977). Lifting idempotents and exchange rings. Trans. Am. Math. Soc. 229:269–278. DOI: 10.1090/S0002-9947-1977-0439876-2.
  • Tuganbaev, A. A. (2000). Rings whose nonzero modules have maximal submodules. J. Math. Sci. 109:1589–1640. DOI: 10.1023/A:1013981125581.
  • Zhang, H. B., Tong, W. (2005). Generalized clean rings. J. Nanjing Univ. Math. Biquarterly. 22:183–188.

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