Advertisement

Czechoslovak Mathematical Journal

, Volume 58, Issue 4, pp 899–910 | Cite as

Exchange rings in which all regular elements are one-sided unit-regular

  • Huanyin Chen
Article

Abstract

Let R be an exchange ring in which all regular elements are one-sided unit-regular. Then every regular element in R is the sum of an idempotent and a one-sided unit. Furthermore, we extend this result to exchange rings satisfying related comparability.

Keywords

exchange ring one-sided unit-regularity idempotent 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    P. Ara: Strongly π-regular rings have stable range one. Proc. Amer. Math. Soc. 124 (1996), 3293–3298.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    P. Ara: The exchange property for purely infinite simple rings. Proc. Amer. Math. Soc. 132 (2004), 2543–2547.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    P. Ara, K. R. Goodearl, K. C. O’Meara and E. Pardo: Separative cancellation for projective modules over exchange rings. Israel J. Math. 105 (1998), 105–137.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    P. Ara, K. R. Goodearl and E. Pardo: K 0 of purely infinite simple regular rings. K-Theory 26 (2002), 69–100.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    V. P. Camillo and D. A. Khurana: Characterization of unit regular rings. Comm. Algebra 29 (2001), 2293–2295.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    H. Chen: Elements in one-sided unit regular rings. Comm. Algebra 25 (1997), 2517–2529.MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    H. Chen: Related comparability over exchange rings. Comm. Algebra 27 (1999), 4209–4216.MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    H. Chen: Regular rings, idempotents and products of one-sided units. Comm. Algebra 34 (2006), 737–741.MATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    H. Chen and F. Li: Exchange rings satisfying related comparability. Collect. Math. 53 (2002), 157–164.MATHMathSciNetGoogle Scholar
  10. [10]
    D. Khurana and T. Y. Lam: Clean matrices and unit-regular matrices. J. Algebra 280 (2004), 683–698.MATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    T. Y. Lam: A crash course on stable range, cancellation, substitution and exchange. J. Algebra Appl. 3 (2004), 301–343.MATHCrossRefMathSciNetGoogle Scholar
  12. [12]
    D. Lu, Q. Li and W. Tong: Comparability, stability, and completions of ideals. Comm. Algebra 32 (2004), 2617–2634.MATHCrossRefMathSciNetGoogle Scholar
  13. [13]
    W. K. Nicholson and Y. Zhou: Clean rings: A survey, Advances in Ring Theory. Proceedings of the 4th China-Japan-Korea International Conference, 2004, pp. 181–198.Google Scholar
  14. [14]
    E. Pardo: Comparability, separativity, and exchange rings. Comm. Algebra 24 (1996), 2915–2929.MATHCrossRefMathSciNetGoogle Scholar
  15. [15]
    J. Wei: Unit-regularity and stable range conditions. Comm. Algebra 33 (2005), 1937–1946.MATHCrossRefMathSciNetGoogle Scholar
  16. [16]
    A. A. Tuganbaev: Rings Close to Regular. Kluwer Academic Publishers, Dordrecht, Boston, London, 2002.MATHGoogle Scholar

Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2008

Authors and Affiliations

  1. 1.Hangzhou Normal UniversityHangzhouPeople’s Republic of China

Personalised recommendations