Skip to main content
SpringerLink
Log in

An Axiomization for Cubic Algebras

  • Chapter
Mathematical Essays in honor of Gian-Carlo Rota

Part of the book series: Progress in Mathematics ((PM,volume 161))

  • 624 Accesses

Abstract

We provide a list of universal axioms for cubic algebras inside the variety of implication algebras. This list is shown to axiomatize the subvariety generated by cubic algebras.

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

Access this chapter

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 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abbott, J.C. Sets, Lattices, and Boolean Algebras Allyn and Bacon, Boston, MA, 1969.

    MATH  Google Scholar 

  2. Bennet, M.K. The face lattice of an n-dimensional cube Algebra Universalis 14 (1982), 82–86.

    Article  MathSciNet  Google Scholar 

  3. Birkhoff, G. Lattice Theory AMS Colloquium Publications, Vol.25, Providence RI, 1979.

    MATH  Google Scholar 

  4. Bailey, C.G. Free Cubic Algebras in preparation.

    Google Scholar 

  5. Bailey, C.G. and Oliveira, J.S. Cubic lattices preprint.

    Google Scholar 

  6. Chen, W.Y.C. and Oliveira, J.S. Implication Algebras and the Metropolis-Rota Axioms for Cubic Lattices preprint.

    Google Scholar 

  7. Metropolis, N. and Rota, G.-C. Combinatorial Structure of the Faces of the n-cube, SIAM J. Appl. Math 35 (1978), 689–694.

    Article  MathSciNet  MATH  Google Scholar 

  8. Oliveira, J.S. The Theory of Cubic Lattices Ph.D. thesis, MIT, 1992.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematical and Computing Sciences, Victoria University of Wellington, Wellington, New Zealand

    Colin Bailey & Joseph Oliveira

  2. UCSF Medical School, San Francisco, USA

    Colin Bailey & Joseph Oliveira

Authors
  1. Colin Bailey
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Joseph Oliveira
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics, Michigan State University, 48824, East Lansing, MI, USA

    Bruce E. Sagan

  2. Department of Mathematics, MIT, 02139, Cambridge, MA, USA

    Richard P. Stanley

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Birkhäuser

About this chapter

Cite this chapter

Bailey, C., Oliveira, J. (1998). An Axiomization for Cubic Algebras. In: Sagan, B.E., Stanley, R.P. (eds) Mathematical Essays in honor of Gian-Carlo Rota. Progress in Mathematics, vol 161. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4108-9_16

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-4108-9_16

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-8656-1

  • Online ISBN: 978-1-4612-4108-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation