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SOME STUDIES ON 2-PRIMAL RINGS, (S,1)-RINGS AND THE CONDITION (KJ)

Matsuoka, Manabu

  • Received : 2009.09.11
  • Published : 2010.07.31

Abstract

In this paper we study the connection between 2-primal rings, (S,1)-rings and related conditions. And we investigate some condition which is the special case of pseudo symmetric. We also study the condition (KJ) which is given by J. Y. Kim and H. L. Jin. We introduce some condition and we prove that our condition is equivalent to the condition (KJ) when it is an (S,1)-ring.

Keywords

2-primal rings;(S,1)-rings;condition (KJ)

References

  1. G. F. Birkenmeier, H. E. Heatherly, and E. K. Lee, Completely prime ideals and associated radicals, Ring theory (Granville, OH, 1992), 102–129, World Sci. Publ., River Edge, NJ, 1993.
  2. Y. Hirano, Some studies on strongly ${\pi}-regular$ rings, Math. J. Okayama Univ. 20 (1978), no. 2, 141–149.
  3. S. U. Hwang, Y. C. Jeon, and Y. Lee, Structure and topological conditions of NI rings, J. Algebra 302 (2006), no. 1, 186–199. https://doi.org/10.1016/j.jalgebra.2006.02.032
  4. C. O. Kim, H. K. Kim, and S. H. Jang, A study on quasi-duo rings, Bull. Korean Math. Soc. 36 (1999), no. 3, 579–588.
  5. J. Y. Kim and H. L. Jin, On weak ${\pi}-regularity$ and the simplicity of prime factor rings, Bull. Korean Math. Soc. 44 (2007), no. 1, 151–156. https://doi.org/10.4134/BKMS.2007.44.1.151
  6. N. K. Kim and Y. Lee, On right quasi-duo rings which are ${\pi}-regular$, Bull. Korean Math. Soc. 37 (2000), no. 2, 217–227.
  7. G. Shin, Prime ideals and sheaf representation of a pseudo symmetric ring, Trans. Amer. Math. Soc. 184 (1973), 43–60. https://doi.org/10.1090/S0002-9947-1973-0338058-9