Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On Left SF-Rings and Strongly Regular Rings

  • Received : 2015.09.08
  • Accepted : 2016.03.11
  • Published : 2016.09.23
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Abstract

A ring R called left SF if its simple left modules are at. Regular rings are known to be left SF-rings. However, till date it is unknown whether a left SF-ring is necessarily regular. In this paper, we prove the strong regularity of left (right) complement bounded left SF-rings. We also prove the strong regularity of a class of generalized semi-commutative left SF-rings.

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References

  1. H. E. Abulkheir and G. F. Birkenmeier, Right complement bounded semiprime rings, Acta. Math. Hungar., 70(3)(1996), 227-235. https://doi.org/10.1007/BF02188209
  2. V. S. Ramamurthy, On the injectivity and atness of certain cyclic modules, Proc. Amer. Math. Soc., 48(1975), 21-25. https://doi.org/10.1090/S0002-9939-1975-0354779-3
  3. M. B. Rege, On von Neumann regular rings and SF-rings, Math. Japonica, 31(6)(1986), 927-936.
  4. Y. Xiao, One sided SF-rings with certain chain conditions, Canad. Math. Bull, 37(2)(1994), 272-277. https://doi.org/10.4153/CMB-1994-040-8
  5. R. Yue Chi Ming, Annihilators and strongly regular rings, Rend. Sem.Fac. Sc. Univ. Cagliari, 57(1987), 51-59 .
  6. R. Yue Chi Ming, On Von Neumann regular rings XV, Acta Mathematica Vietnamica, 23(1988), 71-79.
  7. R. Yue. Chi Ming: On rings close to regular and p-injectivity, Commentationes Mathematicae Universitatis, 47(2)(2006), 203-212.
  8. J. Zhang and X. Du, Left SF-rings whose complement left ideals are ideals, Acta Mathematica Vietnamica, 17(1)(1992), 157-159.
  9. J. Zhang and X. Du, Von Neumann regularity of SF-rings, Communications in Algebra, 21(7)(1993), 2445-2451. https://doi.org/10.1080/00927879308824685
  10. J. Zhang and R. Lu, Strongly regular rings and SF-rings, Northeast. Math. J., 14(1)(1998), 61-68.
  11. H. Zhou, Left SF-rings and regular rings, Communications in Algebra, 35(2007), 3842-3850. https://doi.org/10.1080/00927870701511632