Skip to main content
SpringerLink
Log in

On a generalization of principal weak flatness property

  • RESEARCH ARTICLE
  • Published:
Semigroup Forum Aims and scope Submit manuscript

Abstract

In this article a generalization of principal weak flatness of acts is defined. Using this new property the characterization of some new classes of monoids are investigated. Furthermore, many known results are generalized.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bulman-Fleming, S.: Flat and strongly flat S-systems. Commun. Algebra 20, 2553–2567 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bulman-Fleming, S., McDowell, K.: Monoids over which all weakly flat acts are flat. Proc. Edinb. Math. Soc. 33, 287–298 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bulman-Fleming, S., Kilp, M., Laan, V.: Pullbacks and flatness properties of acts. Part II. Commun. Algebra 29, 851–878 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  4. Edwards, P.M.: Eventually regular semigroups. Bull. Aust. Math. Soc. 28, 23–38 (1983)

    Article  MATH  Google Scholar 

  5. Gould, V.A.R.: Divisible S-systems and R-modules. Proc. Edinb. Math. Soc. 2(30), 187–200 (1987)

    Article  Google Scholar 

  6. Howie, M.: Fundamentals of Semigroup Theory. Oxford Science Publications, Oxford (1995), p. 351

    MATH  Google Scholar 

  7. Kilp, M., Knauer, U., Mikhalev, A.: Characterization of monoids by properties of their left Rees factors. Tartu Toim. 640, 29–37 (1983) (in Russian)

    Google Scholar 

  8. Kilp, M., Knauer, U., Mikhalev, A.: Monoids, Acts and Categories. de Gruyter, Berlin (2000)

    Book  MATH  Google Scholar 

  9. Laan, V.: When torsion free acts are principally wakly flat. Semigroup Forum 60, 321–325 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  10. Laan, V.: Pullbacks and flatness properties of acts. Part I. Commun. Algebra 29, 829–850 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  11. Qiao, H.S.: Some new characterizations of right cancellative monoids by condition (PWP). Semigroup Forum 71, 134–139 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Qiao, H.S., Wang, L.M., Liu, Z.K.: On some new characterizations of right cancellative monoids by flatness properties. Arab. J. Sci. Eng. 32, 75–82 (2007)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors would like to appreciate the anonymous referee for many helpful comments and suggestions. This research was supported by NSFC (No. 10901129, No. 11101197, No. 11001222), SRFDP (20096203120001), Research Supervisor Program of Education Department of Gansu Province (0801-03), and NWNU-KJCXGC-03-51.

Author information

Authors and Affiliations

  1. College of Mathematics and Information Science, Northwest Normal University, Lanzhou, 730070, Gansu, China

    Husheng Qiao & Chongqing Wei

Authors
  1. Husheng Qiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chongqing Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Husheng Qiao.

Additional information

Communicated by Steve Pride.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Qiao, H., Wei, C. On a generalization of principal weak flatness property. Semigroup Forum 85, 147–159 (2012). https://doi.org/10.1007/s00233-012-9387-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00233-012-9387-1

Keywords

Search

Navigation