• Kim, Nam-Kyun (Department of Mathematics, Kyung Hee University) ;
  • Lee, Yang (Department of Mathematics Education, Pusan National University)
  • Published : 2000.05.01


This paper is motivated by the results in [2], [10], [13] and [19]. We study some properties of generalizations of commutative rings and relations between them. We also show that for a right quasi-duo right weakly ${\pi}-regular$ ring R, R is an (S,2)-ring if and only if every idempotent in R is a sum of two units in R, which gives a generalization of [2, Theorem 4] on right quasi-duo rings. Moreover we find a condition which is equivalent to the strongly ${\pi}-regularity$ of an abelian right quasi-duo ring.


quasi-duo ring;${\pi}-regular$ ring;(S, 2)-ring and 2-primal ring


  1. J. Pure and Applied Algebra v.76 Noncommutative rings in which every prime ideal is contained in a unique maximal ideal S.-H. Sun
  2. Trans. Amer. Math. Soc. v.184 Prime ideals and sheaf representation of a pseudo symmetric ring G. Shin
  3. Some results on quasi-duo rings
  4. Comm. Algebra. v.26 no.2 Questions on 2-primal rings Y. Lee;C. Huh;H.K. Kim
  5. Bull. Korean Math. Soc. v.36 no.3 A study on quasi-duo rings C.O. Kim;H.K. Kim;S.H. Jang
  6. Von Neumann Regular Rings K.R. Goodearl
  7. J. Fac. Sic. Hokkaido Univ. v.13 Strongly π-regular rings G. Azumaya
  8. Lectures on Rings and Modules J. Lambek
  9. Proc. Biennial Ohio State-Denison Conference 1992 Completely prime ideals and associated radicals G.F. Birkenmeier;H.E. Heatherly;E.K. Lee;S.K. Jain(ed.);S.T. Rizvi(ed.)
  10. Comm. Algebra v.22 no.1 On semicommutative π-regular rings A. Badawi
  11. Glasgow Math. J. v.37 On quasi-duo rings H.-P. Yu
  12. Trans. Amer. Math. Soc. v.95 Finitistic dimension and a generalizations of semiprimary rings H. Bass
  13. C. R. Acad. Sci. Paris. Ser. A. v.283 Sur les anneaux fortement π-reguliers F. Dischinger
  14. J. Appl. Algebra On weak π-regularity of rings whose prime ideals are maximal C.T. Hong;N.K. Kim;T.K. Kwak;Y. Lee
  15. J. Pure and Appl. Algebra. v.155 Regularity conditions and the simplicity of prime factor rings G.F. Birkenmeier;J.Y. Kim;J.K. Park
  16. J. Algebra v.69 Rings generated by units J.W. Fisher;R. Snider
  17. Math. J. Okayama Univ. v.20 Some studies on strongly π-regular rings Y. Hirano
  18. Pure Appl. Math. Sci. v.21 Weakly right duo rings X. Yao
  19. Kyungpook Math. J. v.38 no.1 A note on π-regular rings Y. Lee;C. Huh