Skip to main content
SpringerLink
Log in
Book cover

International Conference on Relational Methods in Computer Science

RelMiCS 2003: Relational and Kleene-Algebraic Methods in Computer Science pp 171–177Cite as

A Note on Complex Algebras of Semigroups

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3051))

Abstract

The main result is that the variety generated by complex algebras of (commutative) semigroups is not finitely based. It is shown that this variety coincides with the variety generated by complex algebras of partial (commutative) semigroups. An example is given of an 8-element commutative Boolean semigroup that is not in this variety, and an analysis of all smaller Boolean semigroups shows that there is no smaller example. However, without associativity the situation is quite different: the variety generated by complex algebras of (commutative) binars is finitely based and is equal to the variety of all Boolean algebras with a (commutative) binary operator.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andreka, H.: Representations of distributive lattice ordered semigroups with binary relations. Algebra Universalis 28, 12–25 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  2. Henkin, L., Monk, J.D., Tarski, A.: Cylindric algebras, Part II. North-Holland, Amsterdam (1985)

    MATH  Google Scholar 

  3. Hirsch, R., Hodkinson, I.: Step by step — building representations in algebraic logic. J. Symbolic Logic 62, 816–847 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  4. Hirsch, R., Hodkinson, I.: Relation algebras by games. Studies in Logic and the Foundations of Mathematics, vol. 147. Elsevier Science, North-Holland (2002)

    MATH  Google Scholar 

  5. Jipsen, P.: Computer aided investigations of relation algebras, dissertation, Vanderbilt University (1992), www.chapman.edu/~jipsen/dissertation/

  6. Jipsen, P., Maddux, R.D.: Nonrepresentable sequential algebras. Log. J. IGPL 5(4), 565–574 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  7. Maddux, R.D.: Nonfinite axiomatizability results for cylindric and relation algebras. J. Symbolic Logic 54(3), 951–974 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  8. Monk, D.: On representable relation algebras. Michigan Math. J. 11, 207–210 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  9. Reich, P.: Complex algebras of semigroups, dissertation, Iowa State University (1996)

    Google Scholar 

  10. Tarski, A.: On the calculus of relations. J. Symbolic Logic 6, 73–89 (1941)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Chapman University, Orange, CA, 92866, USA

    Peter Jipsen

Authors
  1. Peter Jipsen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Informatik, Christian-Albrechts-Universität Kiel, Olshausenstraße 40, 24098, Kiel, Germany

    Rudolf Berghammer

  2. Institute of Computer Science, University of Augsburg,  

    Bernhard Möller

  3. Department of Computer Science, University of Sheffield, United Kingdom

    Georg Struth

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Jipsen, P. (2004). A Note on Complex Algebras of Semigroups. In: Berghammer, R., Möller, B., Struth, G. (eds) Relational and Kleene-Algebraic Methods in Computer Science. RelMiCS 2003. Lecture Notes in Computer Science, vol 3051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24771-5_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-24771-5_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22145-6

  • Online ISBN: 978-3-540-24771-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation