DOI QR코드

DOI QR Code

RINGS WHOSE PRIME RADICALS ARE COMPLETELY PRIME

KANG, KWANG-HO;KIM, BYUNG-OK;NAM, SANG-JIG;SOHN, SU-HO

  • 발행 : 2005.07.01

초록

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.

키워드

prime radical;completely 2-primal ring;2-primal ring

참고문헌

  1. G. Azumaya, Strongly $\pi$-reqular rings, J. Fac. Sci. Hokkaido Univ. 13 (1954), 34-39
  2. 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
  3. F. Dischinger, Sur les anneauxfortement ti-requliers, C. R. Acad. Sci. Paris, Ser. A 283 (1976), 571-573
  4. 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 https://doi.org/10.2140/pjm.1974.54.135
  5. I. N. Herstein, Topics in Ring Theory, The University of Chicago Press, ChicagoLondon, 1965
  6. Y. Hirano, Some studies on strongly n-reqular rings, Math. J. Okayama Univ. 20 (1978), 141-149
  7. C. Y. Hong and T. K. Kwak, On minimal strongly prime ideals, Comm. Algebra 28 (2000), no. 10, 4867-4878 https://doi.org/10.1080/00927870008827127
  8. C. Huh, E. J. Kim, H. K. Kim, and Y. Lee, Nilradicals of power series rings and nil power series rings, submitted
  9. 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
  10. A. A. Klein, Rings of bounded index, Comm. Algebra 12 (1984), no. 1, 9-21 https://doi.org/10.1080/00927878408822986
  11. Y. Lee, C. Huh, and H. K. Kim, Questions on 2-primal rings, Comm. Algebra 26 (1998), no. 2, 595-600 https://doi.org/10.1080/00927879808826150
  12. L. H. Rowen, Ring Theory, Academic Press, Inc., San Diego, 1991
  13. G. Shin, Prime ideals and sheaf representation of a pseudo symmetric rings, Trans. Amer. Math. Soc. 184 (1973), 43-60 https://doi.org/10.2307/1996398
  14. R. Baer, Radical ideals, Amer. J. Math. 65 (1943), 537-568 https://doi.org/10.2307/2371865