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Special-valued l-groups and Abelian covers

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Abstract

This paper presents a new and independent proof of the theorem (proven first by Kopytov and Gurchenkov [7] and again by Reilly [10]) that covers of the Abelian l-variety are either representable or are Scrimger covers. The proof in this paper is based upon the l-Cauchy constructions of Ball [1]; once these are applied to the problem, the proof becomes elementary.

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References

  1. R. N. Ball (1980) Convergence and Cauchy structures on lattice-ordered groups, Trans. Amer. Math. Soc. 259, 357–391.

    Google Scholar 

  2. R. N. Ball, P. Conrad, and M. Darnel (1986) Above and below subgroups of a lattice-ordered group, Trans. Amer. Math. Soc. 297, 1–40.

    Google Scholar 

  3. A. Bigard, K. Keimel, and S. Wolfenstein (1977) Groupes et Anneaux Reticulés, Lecture Notes in Mathematics, No. 608, Springer-Verlag, New York.

    Google Scholar 

  4. J. P. Bixler and M. Darnel (1986) Special-valued l-groups, Algebra Universalis 22, 172–191.

    Google Scholar 

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

    Google Scholar 

  6. S. A. Gurchenkov (1982) Minimal varieties of l-groups, Algebra i Logika, 21 (2), 131–137.

    Google Scholar 

  7. S. A. Gurchenkov and V. Kopytov (1987) On covers of the variety of Abelian lattice-ordered groups, Siberian Math. J. 28 (3),

    Google Scholar 

  8. W. C. Holland (1976) The largest proper variety of lattice-ordered groups, Proc. Amer. Math. Soc. 57, 25–28.

    Google Scholar 

  9. N. Ya. Medvedev (1977) The lattices of varieties of lattice-ordered groups and Lie algebras, Algebra i Logika 16 (1), 40–45.

    Google Scholar 

  10. N. Reilly (1986) Varieties of lattice-ordered groups that contain no Abelian o-groups are solvable, Order, 3, 287–297.

    Google Scholar 

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

    Google Scholar 

  12. J. E. Smith (1980) The lattice of l-group varieties, Trans. Amer. Math. Soc. 257, 347–357.

    Google Scholar 

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Authors and Affiliations

  1. Division of Arts and Sciences, Indiana University at South Bend, P.O. Box 7111, 46634, South Bend, IN, U.S.A.

    Michael Darnel

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  1. Michael Darnel
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Communicated by A. M. W. Glass

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Darnel, M. Special-valued l-groups and Abelian covers. Order 4, 191–194 (1987). https://doi.org/10.1007/BF00337696

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  • DOI: https://doi.org/10.1007/BF00337696

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