Periodica Mathematica Hungarica

, Volume 20, Issue 2, pp 155–160 | Cite as

Meet-regular intervals in lattices of finite length

  • M. Stern
Article
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Mathematics subject classification numbers, 1980/1985

Primary 06B05 Secondary 06C10 

Key words and phrases

Lattice of finite length join-regular (meet-regular) interval complementedness semimodularity 
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References

  1. [1]
    G. Birkhoff,Lattice theory (third edition), American Math. Society, Providence (R. I.), 1967.MR 37: 2638Google Scholar
  2. [2]
    A. Björner, Homotopy type of posets and lattice complementation,J. Combin. Theory Ser. A. 30 (1981), 90–100.MR 82k: 06001CrossRefGoogle Scholar
  3. [3]
    A. Björner, On complements in lattices of finite length,Discrete Math. 36 (1981), 325–326.MR 84b: 06010CrossRefGoogle Scholar
  4. [4]
    A. Björner andI. Rival, A note on fixed points in semimodular lattices,Discrete Math. 29 (1980), 245–250.MR 81d: 06010CrossRefGoogle Scholar
  5. [5]
    P. Crawley andR. P. Dilworth,Algebraic theory of lattices, Prentice-Hall, Englewood Cliffs (N. J.), 1973.RŽMat 1974: 10A289Google Scholar
  6. [6]
    G. Grätzer,Universal algebra (second edition), Springer, New York, 1979.MR 40: 1320;80g: 08001Google Scholar
  7. [7]
    G. Grätzer,General lattice theory, Birkhäuser, Basel, 1978.MR 80c: 06001Google Scholar
  8. [8]
    J. Kalman, A property of algebraic lattices whose compact elements have complements,Algebra Universalis 22 (1986), 100–101.Zbl 597: 06004CrossRefGoogle Scholar
  9. [9]
    B. Stenström, Radicals and socles of lattices,Arch. Math. (Basel)20 (1969), 258–261.MR 39: 6769Google Scholar
  10. [10]
    M. Stern, On radicals in lattices,Acta Sci. Math. (Szeged)38 (1976), 157–164.MR 53: 10672Google Scholar
  11. [11]
    M. Stern, On complemented modular lattices of finite length, Martin-Luther-Universität, Halle, 1987. (Preprint der Sektion Mathematik, No. 95)Google Scholar
  12. [12]
    M. Stern, On complements in lattices with covering properties, Martin-Luther-Universität, Halle, 1987. (Preprint der Sektion Mathematik, No. 103)Google Scholar
  13. [13]
    G. Szász,Einführung in die Verbandstheorie, Teubner, Leipzig, 1962.MR 22: 1527;25: 2011Google Scholar

Copyright information

© Akadémiai Kiadó 1989

Authors and Affiliations

  • M. Stern
    • 1
  1. 1.Martin-Luther-Universität Sektion MathematikHalle (Saale)German Democratic Republic

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