Skip to main content
SpringerLink
Log in

Free split bands

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

Abstract

We solve the word problem for the free objects in the variety consisting of bands with a semilattice transversal. It follows that every free band can be embedded into a band with a semilattice transversal.

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

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Gerhard, J.A.: The lattice of equational classes of idempotent semigroups. J. Algebra 15, 195–224 (1970)

    Article  MATH  MathSciNet  Google Scholar 

  2. Green, J.A., Rees, D.: On semigroups in which \(x^{r}=x\). Proc. Camb. Philos. Soc. 48, 35–40 (1952)

    Article  MATH  MathSciNet  Google Scholar 

  3. Howie, J.M.: Fundamentals of Semigroup Theory. Clarendon Press, Oxford (1995)

    MATH  Google Scholar 

  4. McAlister, D.B., Blyth, T.S.: Split orthodox semigroups. J. Algebra 51, 491–525 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  5. McLean, D.: Idempotent semigroups. Am. Math. Mon 61, 110–113 (1954)

    Article  MATH  MathSciNet  Google Scholar 

  6. Petrich, M.: Lectures in Semigroups. Akademie-Verlag, Berlin (1977)

    Google Scholar 

  7. Saito, T.: A note on regular semigroups with inverse transversals. Semigroup Forum 33, 149–152 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  8. Tang, X.: LRT-biordered sets. Semigroup Forum 73, 377–394 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  9. Yoshida, R.: Right regular bands with semilattice transversals; In: Proceedings of the 8th Symposium on Semigroups, Shimane University, Matsue, Pp. 26–31 (1984)

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, WI , 53233, USA

    Francis Pastijn & Justin Albert

Authors
  1. Francis Pastijn
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Justin Albert
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Justin Albert.

Additional information

Communicated by László Márki.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pastijn, F., Albert, J. Free split bands. Semigroup Forum 90, 753–762 (2015). https://doi.org/10.1007/s00233-014-9625-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00233-014-9625-9

Keywords

Search

Navigation