Skip to main content
Log in

Semilattice transversals of regular bands II

  • Research Article
  • Published:
Semigroup Forum Aims and scope Submit manuscript

Abstract

A band is a regular band if and only if it can be embedded into a band in which every element belongs to a semilattice transversal.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Albert, J.: Bands with high symmetry and uniform bands. Doctoral dissertation, Marquette University, Milwaukee (2012)

  2. Buekenhout, F., Huybrechts, C., Pasini, A.: Parallelism in diagram geometry. Bull. Belg. Math. Soc. 3, 355–397 (1994)

    MATH  MathSciNet  Google Scholar 

  3. Buekenhout, F., Cohen, A.M.: Diagram Geometry. Springer, New York (2013)

    Book  MATH  Google Scholar 

  4. Clifford, A.H., Preston, G.B.: The Algebraic Theory of Semigroups I. American Mathematical Society, Providence (1961)

    MATH  Google Scholar 

  5. Clifford, A.H., Preston, G.B.: The Algebraic Theory of Semigroups II. American Mathematical Society, Providence (1967)

    MATH  Google Scholar 

  6. Dembowski, P.: Finite Geometries. Springer, New York (1968)

    Book  MATH  Google Scholar 

  7. Gorbunov, V.A.: Algebraic Theory of Quasivarieties. Plenum Publishing Corporation, New York (1998)

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  9. Janowitz, M.F.: Baer semigroups. Duke Math. J. 32, 95–95 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  10. Janowitz, M.F.: A semigroup approach to lattices. Can. J. Math. 18, 1212–1223 (1966)

    Article  MATH  MathSciNet  Google Scholar 

  11. Kimura, N.: The structure of idempotent semigroups (I). Pac. J. Math. 8, 257–275 (1958)

    Article  MATH  MathSciNet  Google Scholar 

  12. McKenzie, R.N., McNulty, G.F., Taylor, W.F.: Algebras, Lattices, Varieties, vol. I. Wadsworth & Brooks/Cole, Monterey (1987)

    MATH  Google Scholar 

  13. Nambooripad, K.S.S.: Structure of Regular Semigroups I. Memoirs of the American Mathematical Society, No. 224, Providence (1979)

  14. Pastijn, F.: Biordered sets and complemented modular lattices. Semigroup Forum 21, 205–220 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  15. Pastijn, F., Albert, J.: Free split bands. Semigroup Forum 90, 753–762 (2015)

    Article  MATH  MathSciNet  Google Scholar 

  16. Pastijn, F., Albert, J.: Semilattice transversals of regular bands I. Commun. Algebra 45(11), 4979–4991 (2017)

    Article  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  18. Shrikhande, S.S.: Affine resolvable balanced incomplete block designs. A survey. Aequ. Math. 14(3), 251–269 (1980)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Francis Pastijn.

Additional information

Communicated by Marcel Jackson.

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. Semilattice transversals of regular bands II. Semigroup Forum 95, 423–440 (2017). https://doi.org/10.1007/s00233-017-9863-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00233-017-9863-8

Keywords

Navigation