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A survey of varieties of lattice ordered groups

Part of the Lecture Notes in Mathematics book series (LNM,volume 1004)

Keywords

  • Abelian Variety
  • Lattice Operation
  • Irreducible Variety
  • Convex Subgroup
  • Pointwise Order

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. G. Birkhoff, Lattice Theory, Amer. Math. Soc. Colloquium Pub. vol. 25, (1969).

    Google Scholar 

  2. A. Bigard, K. Keimel, and S. Wolfenstein, Groupes et Anneaux Réticulés, Lecture Notes in Mathematics 608, Springer, (1977).

    Google Scholar 

  3. The Black Swamp Problem Book, unpublished, original kept at Bowling Green State University.

    Google Scholar 

  4. T. Feil, An uncountable tower of l-group varieties, Algebra Universalis, 14 (1981), 129–131.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. L. Fuchs, Partially Ordered Algebraic Systems, Addison Wesley (1963).

    Google Scholar 

  6. A. M. W. Glass, Ordered Permutation Groups, London Math. Soc. Lecture Notes 55, Cambridge U. Press, (1981).

    Google Scholar 

  7. A. M. W. Glass, W. C. Holland, S. H. McCleary, The structure of l-group varieties, Algebra Universalis, 10(1980), 1–20.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. W. C. Holland, The lattice ordered group of automorphisms of an ordered set, Michigan Math. J., 10(1963), 399–408.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. _____, The largest proper variety of lattice ordered groups, Proc. Amer. Math. Soc., 57(1976), 25–28.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. _____, Varieties of l-groups are torsion classes, Czech. Math. J., 29 (1979), 11–12.

    MathSciNet  MATH  Google Scholar 

  11. H. A. Hollister, Nilpotent l-groups are representable, Algebra Universalis, 8 (1978), 65–71.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. V. M. Kopytov and N. Ja. Medvedev, Varieties of lattice ordered groups, Algebra and Logic, 16(1977), 281–285.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. P. Lorenzen, Über halbgeordnete Gruppen, Math. Z., 52(1950), 483–526.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. J. Martinez, Free products in varieties of lattice-ordered groups, Czech. Math. J., 22(1972), 535–553.

    MathSciNet  MATH  Google Scholar 

  15. _____, Archimedean-like classes of lattice-ordered groups, Trans. Amer. Math. Soc., 186(1973), 33–49.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. _____, Varieties of lattice-ordered groups, Math. Z., 137(1974), 265–284.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. S. H. McCleary, O-primitive ordered permutation groups I, II, Pacific J. Math., 40(1972), 349–372; 49(1973), 431–443.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. N. Ja. Medvedev, The lattices of varieties of lattice ordered groups and Lie algebras, Algebra and Logic, 16(1977), 27–30.

    CrossRef  MATH  Google Scholar 

  19. N. R. Reilly, A subsemilattice of the lattice of varieties of lattice ordered groups, Can. J. Math., 33(1981), 1309–1318.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. E. B. Scrimger, A large class of small varieties of lattice ordered groups, Proc. Amer. Math. Soc., 51(1975), 301–306.

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. E. C. Weinberg, Free lattice-ordered groups, Math. Ann., 151(1963), 187–199.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1983 Springer-Verlag

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Holland, W.C. (1983). A survey of varieties of lattice ordered groups. In: Freese, R.S., Garcia, O.C. (eds) Universal Algebra and Lattice Theory. Lecture Notes in Mathematics, vol 1004. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0063435

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  • DOI: https://doi.org/10.1007/BFb0063435

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12329-3

  • Online ISBN: 978-3-540-40954-0

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