Skip to main content
SpringerLink
Log in

On Condition (P′)

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

Abstract

Laan in (Acta Comment. Univ. Tartu Math., 2:55–60, 1998) introduced Condition (E′). In Golchin and Mohammadzadeh (Yokohama Math. J., 54:79–88, 2007) we gave a characterization of monoids by this condition of their acts. In this paper similar to Condition (E′), we introduce a generalization of Condition (P) called Condition (P′) and will give a characterization of monoids by this condition of their (Rees factor) acts.

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.: Flatness properties of acts over commutative, cancellative monoids. Mathematica 46, 93–102 (1999)

    MathSciNet  MATH  Google Scholar 

  2. Golchin, A., Renshaw, J.: A flatness property of acts over monoids. In: Conference on Semigroups, University of St. Andrews, July 1997, pp. 72–77 (1998)

    Google Scholar 

  3. Golchin, A., Mohammadzadeh, H.: On condition (E′P). J. Sci. Islam. Repub. Iran 17(4), 343–349 (2006)

    MathSciNet  Google Scholar 

  4. Golchin, A., Mohammadzadeh, H.: On condition (EP). Int. Math. Forum 2(19), 911–918 (2007)

    MathSciNet  MATH  Google Scholar 

  5. Golchin, A., Mohammadzadeh, H.: On homological classification of mono-ids by condition (E′) of right acts. Yokohama Math. J. 54, 79–88 (2007)

    MathSciNet  MATH  Google Scholar 

  6. Howie, J.M.: Fundamentals of Semigroup Theory. London Mathematical Society Monographs. Oxford University Press, London (1995)

    MATH  Google Scholar 

  7. HuSheng, Q.: Some new characterizations of right cancellative monoids by condition (PWP). Semigroup Forum 71, 134–139 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kilp, M., Knauer, U., Mikhalev, A.: Monoids, Acts and Categories: with Applications to Wreath Products and Graphs: a Handbook for Students and Researchers. de Gruyter, Berlin (2000)

    MATH  Google Scholar 

  9. Laan, V.: On a generalization of strong flatness. Acta Comment. Univ. Tartu Math. 2, 55–60 (1998)

    MathSciNet  MATH  Google Scholar 

  10. Laan, V.: Pullbacks and flatness properties of acts. Ph.D Thesis, Tartu (1999)

  11. Laan, V.: On classification of monoids by properties of cofree acts. Semigroup Forum 59, 79–92 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  12. Laan, V.: Pullbacks and flatness properties of acts I. Commun. Algebra 29(2), 829–850 (2001)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the referee for useful and valuable comments and suggestions relating to this article. They would also like to thank professor Steve Pride for providing the communication.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

    Akbar Golchin & Hossein Mohammadzadeh

Authors
  1. Akbar Golchin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hossein Mohammadzadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Akbar Golchin.

Additional information

Communicated by Steve Pride.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Golchin, A., Mohammadzadeh, H. On Condition (P′). Semigroup Forum 86, 413–430 (2013). https://doi.org/10.1007/s00233-012-9441-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00233-012-9441-z

Keywords

Search

Navigation