• KANG, KWANG-HO (Department of Mathematics Busan Science Academy) ;
  • KIM, BYUNG-OK (Department of Mathematics Busan Science Academy) ;
  • NAM, SANG-JIG (Department of Mathematics Busan National University High School) ;
  • SOHN, SU-HO (Department of Mathematics Busan Gukje High School)
  • Published : 2005.07.01


We study in this note rings whose prime radicals are completely prime. We obtain equivalent conditions to the complete 2-primal-ness and observe properties of completely 2-primal rings, finding examples and counterexamples to the situations that occur naturally in the process.


  1. G. Azumaya, Strongly $\pi$-reqular rings, J. Fac. Sci. Hokkaido Univ. 13 (1954), 34-39
  2. R. Baer, Radical ideals, Amer. J. Math. 65 (1943), 537-568
  3. G. F. Birkenmeier, H. E. Heatherly, and E. K. Lee, Completely prime ideals and associated radicals, Proc. Biennial Ohio State-Denison Conference 1992, edited by S. K. Jain and S. T. Rizvi, World Scientific, Singapore-New Jersey-LondonHong Kong, 1993, 102-129
  4. F. Dischinger, Sur les anneauxfortement ti-requliers, C. R. Acad. Sci. Paris, Ser. A 283 (1976), 571-573
  5. J. W. Fisher and R. L. Snider, On the von Neumann regularity of rings with regular prime factor rings, Pacific J. Math. 54 (1974), 135-144
  6. I. N. Herstein, Topics in Ring Theory, The University of Chicago Press, ChicagoLondon, 1965
  7. Y. Hirano, Some studies on strongly n-reqular rings, Math. J. Okayama Univ. 20 (1978), 141-149
  8. C. Y. Hong and T. K. Kwak, On minimal strongly prime ideals, Comm. Algebra 28 (2000), no. 10, 4867-4878
  9. C. Huh, E. J. Kim, H. K. Kim, and Y. Lee, Nilradicals of power series rings and nil power series rings, submitted
  10. C. Huh, H. K. Kim, D. S. Lee, and Y. Lee, Prime radicals of formal power series rings, Bull. Korean Math. Soc. 38 (2001), no. 4, 623-633
  11. A. A. Klein, Rings of bounded index, Comm. Algebra 12 (1984), no. 1, 9-21
  12. Y. Lee, C. Huh, and H. K. Kim, Questions on 2-primal rings, Comm. Algebra 26 (1998), no. 2, 595-600
  13. L. H. Rowen, Ring Theory, Academic Press, Inc., San Diego, 1991
  14. G. Shin, Prime ideals and sheaf representation of a pseudo symmetric rings, Trans. Amer. Math. Soc. 184 (1973), 43-60