Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Some Characterizations of Regular and Semisimple Γ-Rings

  • Ma, Xueling (Department of Mathematics, Hubei Institute for Nationalities) ;
  • Zhan, Jianming (Department of Mathematics, Hubei Institute for Nationalities) ;
  • Jun, Young-Bae (Department of Mathematics Education, Gyeongsang National University)
  • Received : 2010.02.18
  • Accepted : 2010.08.05
  • Published : 2010.09.30
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Abstract

Some characterizations of regular $\Gamma$-rings are described by means of fuzzy ideals. The concepts of fuzzy interior ideals in $\Gamma$-rings and semisimple $\Gamma$-rings are introduced. Some characterizations of semisimple $\Gamma$-rings are investigated by means of fuzzy interior ideals.

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References

  1. W. E. Barnes, On the $\Gamma$-rings of Nobusawa, Pacific J. Math., 18(1966), 411-422. https://doi.org/10.2140/pjm.1966.18.411
  2. B. Davvaz, P. Corsini, Generalized fuzzy hyperideals of hypernear-rings and many valued implications, Journal of Intelligent and Fuzzy Systems, 17(2006), 241-251.
  3. T. K. Dutta, T. Chanda, Structures of fuzzy ideals of $\Gamma$-rings, Bull. Malays. Math. Sci. Soc., 28(1)(2005), 9-15.
  4. S. M. Hong, Y. B. Jun, A note on fuzzy ideals in gamma-rings, Bull. Honam Math. Soc., 12(1995), 39-48.
  5. Y. B. Jun, On fuzzy prime ideals of $\Gamma$-rings, Soochow J. Math., 21(1)(1995), 41-48.
  6. Y. B. Jun, C. Y. Lee, Fuzzy $\Gamma$-rings, Pusan Kyongnan Math. J. (presently, East Asian Math. J.), 8(2)(1992), 163-170.
  7. Y. B. Jun, C. Y. Lee, Fuzzy prime ideals of $\Gamma$-rings, Pusan Kyongnan Math. J. (presently, East Asian Math. J.), 9(1)(1993), 105-111.
  8. H. V. Kumbhojkar, M. S. Bapat, Not-so-fuzzy fuzzy ideals, Fuzzy Sets and Systems, 37(1990), 237-243. https://doi.org/10.1016/0165-0114(90)90046-9
  9. S. Kyuno, N. Nobusawa, N. B. Sith, Regular gamma rings, Tsykuba J. Math., 11(2)(1987), 371-382. https://doi.org/10.21099/tkbjm/1496160588
  10. X. Ma, J. Zhan, Generalized fuzzy h-bi-ideals and h-quasi-ideals of hemirings, Inform. Sci., 179(2009), 1249-1268. https://doi.org/10.1016/j.ins.2008.12.014
  11. T. K. Mukherjee, M. K. Sen, On fuzzy ideals of a ring (I), Fuzzy Sets and Systems, 21(1987), 99-104. https://doi.org/10.1016/0165-0114(87)90155-2
  12. M. A. Ozturk, M. Uckum, Y. B. Jun, Fuzzy ideals in Gamma-rings, Turk. J. Math., 27(2003), 369-374.
  13. M. A. Ozturk, M. Uckum, Y. B. Jun, Characterizations of Artinian and Noetherian gamma-rings in terms of fuzzy ideals, Turk. J. Math., 27(2002), 199-205.
  14. M. M. Rashid, A. C. Paul, Regular gamma rings, Southeast Asian Bull. Math., 31(2007), 933-947.
  15. J. Zhan, W. A. Dudek, Fuzzy h-ideals of hemirings, Inform. Sci., 177(2007), 876-886. https://doi.org/10.1016/j.ins.2006.04.005
  16. J. Zhan, B. Davvaz, K. P. Shum, Generalized fuzzy hyperideals of hyperrings, Comput. Math. Appl., 56(2008), 1732-1740. https://doi.org/10.1016/j.camwa.2008.04.002