Skip to main content
SpringerLink
Log in
Book cover

The Dilworth Theorems pp 237–250Cite as

Birkhäuser

Aspects of distributivity

  • Chapter

  • 346 Accesses

Part of the book series: Contemporary Mathematicians ((CM))

Abstract

A lattice L is distributive if it satisfies the identity

$$a \wedge \left( {b \vee c} \right) = \left( {a \wedge b} \right) \vee \left( {a \wedge c} \right).$$

.

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. G. Birkhoff, On the structure of abstract algebras, Proc. Comb. Phil. Soc., 31 (1935), 433–454.

    Article  Google Scholar 

  2. P. Crawley and R.P. Dilworth, Algebraic theory of lattices, Englewood Cliffs, N.J., Prentice Hall, 1 (1973).

    Google Scholar 

  3. B.A. Davey, W. Poguntke and I. Rival, A characterization of semidistributivity, Alg. Univ. 5 (1975), 72–75.

    Article  Google Scholar 

  4. R.P. Dilworth and P. Crawley, Decomposition theory for lattices without chain conditions, Trans. Amer. Math. Soc., (1960), 1-23.

    Google Scholar 

  5. R.P. Dilworth and J.E. McLaughlin, Distributivity in lattices, Duke Math. J., 19 (1952), 683–694.

    Article  Google Scholar 

  6. R.P. Dilworth, The structure of relatively complemented lattices, Annals of Math., 51 (1950), 348–359.

    Article  Google Scholar 

  7. N. Funayana and T. Nakagama, On the distributivity of a lattice of lattice congruences, Proc. Imp. Acad. Tokyo, 18 (1942), 553–554.

    Article  Google Scholar 

  8. J. Hashimoto, Direct, subdirect decompositions and congruence relations, Osak Math. J., 9 (1957), 87–112.

    Google Scholar 

  9. B. Jónsson, Algebras whose congruence lattices are distributive, Math. Scand., 21 (1967), 110–121.

    Google Scholar 

  10. B. Jónsson, Sublattices of a free lattice, Can. J. Math., 13 (1961), 256–264.

    Article  Google Scholar 

  11. B. Jónsson and I. Rival, Lattice varieties covering the smallest nonmodular variety, Pacific J. Math., 82 (1979), 463–478.

    Article  Google Scholar 

  12. R. McKenzie, Equational bases and nonmodular lattice varieties, Trans. Amer. Math. Soc., 174 (1972), 1–43.

    Article  Google Scholar 

  13. J.B. Nation, Finite sublattices of a free lattice, Trans. Amer. Math. Soc., 269 (1982), 311–337.

    Article  Google Scholar 

  14. Ph. Whitman, Free lattices, Annals of Math., 42 (1941), 325–329.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. California Institute of Technology, Pasadena, California, USA

    R. P. Dilworth

Authors
  1. R. P. Dilworth
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, Dartmouth College, Hanover, NH, 03755, USA

    Kenneth P. Bogart

  2. Department of Mathematics, University of Hawaii, Honolulu, HI, 96822, USA

    Ralph Freese

  3. Department of Mathematics, University of North Texas, Denton, TX, 76203-5116, USA

    Joseph P. S. Kung

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer Science+Business Media New York

About this chapter

Cite this chapter

Dilworth, R.P. (1990). Aspects of distributivity. In: Bogart, K.P., Freese, R., Kung, J.P.S. (eds) The Dilworth Theorems. Contemporary Mathematicians. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-3558-8_23

Download citation

  • DOI: https://doi.org/10.1007/978-1-4899-3558-8_23

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4899-3560-1

  • Online ISBN: 978-1-4899-3558-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation