Skip to main content
SpringerLink
Log in

Some remarks on one-sided regularity

  • Research Article
  • Published:
Frontiers of Mathematics in China Aims and scope Submit manuscript

Abstract

A ring is said to be right (resp., left) regular-duo if every right (resp., left) regular element is regular. The structure of one-sided regular elements is studied in various kinds of rings, especially, upper triangular matrix rings over one-sided Ore domains. We study the structure of (one-sided) regular-duo rings, and the relations between one-sided regular-duo rings and related ring theoretic properties.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Antoine R. Nilpotent elements and Armendariz rings. J Algebra, 2008, 319: 3128–3140

    Article  MathSciNet  MATH  Google Scholar 

  2. Bell H E. Near-rings in which each element is a power of itself. Bull Aust Math Soc, 1970, 2: 363–368

    Article  MathSciNet  MATH  Google Scholar 

  3. Cohn P M. Reversible rings. Bull Lond Math Soc, 1999, 31: 641–648

    Article  MathSciNet  MATH  Google Scholar 

  4. Goodearl K R. Von Neumann Regular Rings. London: Pitman, 1979

    MATH  Google Scholar 

  5. Huh C, Kim N K, Lee Y. Examples of strongly π-regular rings. J Pure Appl Algebra, 2004, 189: 195–210

    Article  MathSciNet  MATH  Google Scholar 

  6. Huh C, Lee Y, Smoktunowicz A. Armendariz rings and semicommutative rings. Comm Algebra, 2002, 30: 751–761

    Article  MathSciNet  MATH  Google Scholar 

  7. Hwang S U, Kim N K, Lee Y. On rings whose right annihilators are bounded. Glasg Math J, 2009, 51: 539–559

    Article  MathSciNet  MATH  Google Scholar 

  8. Jacobson N. Some remarks on one-sided inverses. Proc Amer Math Soc, 1950, 1: 352–355

    Article  MathSciNet  MATH  Google Scholar 

  9. Kwak T K, Lee Y, Seo Y. On commutativity of regular products. Bull Korean Math Soc (to appear)

  10. von Neumann J. On regular rings. Proc Natl Acad Sci USA, 1936, 22: 707–713

    Article  MATH  Google Scholar 

  11. Nielsen P P. Semi-commutativity and the McCoy condition. J Algebra, 2006, 298: 134–141

    Article  MathSciNet  MATH  Google Scholar 

  12. Rege M B, Chhawchharia S. Armendariz rings. Proc Japan Acad Ser A Math Sci, 1997, 73: 14–17

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors thank the referees deeply for their very careful reading of the manuscript and valuable suggestions in depth that improved the paper a lot. The first named author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2016R1D1A1B03931190).

Author information

Authors and Affiliations

  1. Department of Mathematics, Daejin University, Pocheon, 11159, Korea

    Tai Keun Kwak

  2. Institute of Basic Science, Daejin University, Pocheon, 11159, Korea

    Yang Lee

  3. Department of Mathematics, Hanyang University, Seoul, 04763, Korea

    Young Joo Seo

Authors
  1. Tai Keun Kwak
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yang Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Young Joo Seo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tai Keun Kwak.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kwak, T.K., Lee, Y. & Seo, Y.J. Some remarks on one-sided regularity. Front. Math. China 13, 833–847 (2018). https://doi.org/10.1007/s11464-018-0711-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11464-018-0711-2

Keywords

MSC

Search

Navigation