DOI QR코드

DOI QR Code

ON THE MAXIMALITY OE PRIME IDEALS IN EXCHANGE RINGS

  • Published : 2002.07.01

Abstract

We investigate the relationship between various generalizations of von Neumann regularity condition and the condition that every prime ideal is maximal in exchange rings.

Keywords

References

  1. Comm. Algebra v.25 no.4 On abelian π-regular rings A. Badawi https://doi.org/10.1080/00927879708825906
  2. Proc. Biennial Ohio State-Denision Conference Completely prime ideals and associated radicals G. F. Birkenmeier;H. E. HeatherlyE. K. Lee
  3. Proc. Amer. Math. Soc. v.122 A connection between weak regularity and the simplicity of prime factor rings G. F. Birkenmeier;J. Y. Kim;J. K. Park https://doi.org/10.2307/2160840
  4. J. Pure and Appl. Algebra v.115 Regularity conditions and the simplicity of prime factor rings https://doi.org/10.1016/S0022-4049(96)00011-4
  5. Canad. Math. Bull. v.22 Rings all of whose Pierce stalks are local W. K. Burgess;W. Stephenson https://doi.org/10.4153/CMB-1979-022-8
  6. Pacific J. Math. v.14 Refinements for infinite direct decompositions of algebraic systems P. Crawley;B. Jonsson https://doi.org/10.2140/pjm.1964.14.797
  7. Pacific J. Math. v.54 no.1 On the von Beumann regularity of rings with regular prime factor rings J. W. Fisher;R. L. Snider https://doi.org/10.2140/pjm.1974.54.135
  8. Math. J. Okayama Univ. v.20 Some studies on strongly π-regular rings Y. Hirano
  9. Math. J. Okayama Univ. v.32 Some characterizations of π-regular rings of bounded index
  10. Arch. Math. v.66 On rings whose prime radical contains all nilpotent elements of index two Y. Hirano;D. V. Huynh;J. K. Park https://doi.org/10.1007/BF01781553
  11. J. Pure and Applied Algebra v.146 On weak π-regularity of rings whose prime ideals are maximal C. Y. Hong;N. K. Kim;T. K. Kwak;Y. Lee https://doi.org/10.1016/S0022-4049(98)00177-7
  12. Comm. in Algebra v.28 no.10 On minimal strongly prime ideals C. Y. Hong;T. K. Kwak https://doi.org/10.1080/00927870008827127
  13. submitted Some results on quasi-duo rings Y. Lee;C. Huh
  14. Proc. Amer. Math. Soc v.35 A characterization of exchange rings G. S. Monk
  15. Trans. Amer. Math. Soc. v.229 Lifting idempotents and exchange rings W. K. Nicholson https://doi.org/10.2307/1998510
  16. J. Algebra v.103 On rings whose projective modules have the exchange property J. Stock https://doi.org/10.1016/0021-8693(86)90145-6
  17. Comment Math. Helv. v.43 Epimorphismen von kommutativen Ringen H. H. Storrer https://doi.org/10.1007/BF02564404
  18. Math. Ann. v.199 Exchange rings and decompositions of modules R. B. Warfield https://doi.org/10.1007/BF01419573
  19. Pure and Appl. Math. Sci. v.ⅩⅩⅠ no.1-2 Weakly right duo rings Xue Yao
  20. Glasgow Math. J. v.37 On quasi-duo rings H. P. Yu https://doi.org/10.1017/S0017089500030342
  21. Comm. Algebra v.25 no.2 On the structure of exchange rings https://doi.org/10.1080/00927879708825882

Cited by

  1. Exchange Ideals with All Idempotents Central vol.20, pp.04, 2013, https://doi.org/10.1142/S1005386713000618
  2. On Uniquely Clean Rings vol.39, pp.1, 2010, https://doi.org/10.1080/00927870903451959