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Substructures

  • Bjarni Jónsson
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 250)

Keywords

Closure Operator Unary Algebra Modular Lattice Irreducible Element Compact Element 
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Bibliography for Section 3.6

  1. 1.
    G. Birkhoff and O. Frink, "Representations of lattices by sets", Trans. Amer. Math. Soc. 64(1948), 299–316.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    M. Gould, "Multiplicity type and subalgebra structure in universal algebras", Pacific J. of Math. 26(1968), 469–485.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    J. Johnson and R. L. Seifert, "A survey of multi-unary algebras", Mimeographed seminar notes, U. C. Berkeley, 1967, 26 pages.Google Scholar

References for Section 3.8

  1. 1.
    G. Birkhoff, "On the structure of abstract algebras", Proc. Cambridge Philos. Soc. 31(1935), 433–454.CrossRefzbMATHGoogle Scholar
  2. 2.
    — and O. Frink, "Representations of lattices by sets", Trans. Amer. Math. Soc. 64(1948), 299–316.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    W. Hanf, "Representations of lattices by subalgebra (preliminary report)", Bull. Amer. Math. Soc. 62(1956), 402.Google Scholar
  4. 4.
    J. Johnson and R. L. Seifer, "A survey of multi-unary algebras", Mimeographed seminar notes, U. C. Berkeley, 1967, 26 pages.Google Scholar
  5. 5.
    B. Jonsson, "Modular lattices and Desargues' Theorem", Math. Scand. 2(1954), 295–314.MathSciNetzbMATHGoogle Scholar
  6. 6.
    —, "On the representation of lattices", Math. Scand. 1(1953), 193–206.MathSciNetzbMATHGoogle Scholar
  7. 7.
    —, "Representations of modular lattices and relation algebras", Trans. Amer. Math. Soc. 92(1959), 449–464.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    D. Sachs, "The lattice of subalgebras of a Boolean algebra", Canad. J. Math. 14(1962), 451–460.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    T. P. Whaley, "Algebras satisfying the descending chain condition for subalgebras", Thesis, Vanderbilt University, Jan. 1968, 50 pages.Google Scholar
  10. 10.
    P. M. Whitman, "Lattices, equivalence relations and subgroups", Bull. Amer. Math. Soc. 52(1946), 507–522.MathSciNetCrossRefzbMATHGoogle Scholar

References for Section 3.9

  1. 1.
    P. Erdös and A. Hajnal, "On a problem of B. Jonsson", Bull. Acad. Pol. Sci. 14(1966), 19–23.MathSciNetzbMATHGoogle Scholar
  2. 2.
    P. Erdös, A. Hajnal and R. Rado, "Partition relations for cardinal numbers", Acta Mathematica (Acad. Sci. Hung.) 16(1965), 93–196.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    A. Hajnal, "Proof of a conjecture of S. Ruziewicz", Fund. Math. 50(1961), 123–128.MathSciNetzbMATHGoogle Scholar
  4. 4.
    H. J. Keisler and F. Rowbottom, "Constructible sets and weakly compact cardinals", Notices Amer. Math. Soc. 12(1965), 373–374.Google Scholar
  5. 5.
    A. Kostinsky and R. McKenzie, "Cardinality problems for rings", Notices Amer. Math. Soc. 15(1968), 389.Google Scholar
  6. 6.
    S. P. Strunkov, "Subgroups of periodic groups", Soviet-Mathematics Doklady 7(1966), 1201–1203.zbMATHGoogle Scholar
  7. 7.
    T. Whaley, "Algebras satisfying the descending chain condition for subalgebras", Thesis, Vanderbilt University, 1968, 50 pages.Google Scholar
  8. 8.
    —, "Infinite algebras satisfying the descending chain condition", Notices Amer. Math. Soc. 14(1967), 714.Google Scholar

References for Section 3.10

  1. 1.
    M. Gould and C. Platt, "Versatile monoids and versatile categories", Preliminary report, 17 pp.Google Scholar
  2. 2.
    M. Makkai, "Solution of a problem of G. Grätzer concerning endomorphism semigroups", Acta Math. Acad. Sci. Hungar. 15(1964), 297–307.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    E. T. Schmidt, "Universale Algebren mit gegebenen Automorphismengruppen und Unteralgebraverbänden", Acta Sci. Math. (Szeged) 24(1963), 251–254.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1972

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  • Bjarni Jónsson

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