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A variety of lattice-ordered groups containing all representable covers of the abelian variety

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Abstract

A small variety of representable lattice-ordered groups is constructed, which contains all of the representable covers of the abelian variety.

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References

  1. M.Anderson and T.Feil (1988) Lattice-Ordered Groups: An Introduction, D. Reidel, Dordecht, Holland.

    Google Scholar 

  2. G.Bergman (1984) Specially ordered groups, Comm. Algebra 12, 2315–1333.

    Article  Google Scholar 

  3. C. G.Chehata (1952) An algebraically simple ordered group, Proc. London Math. Soc. 2, 183–197.

    Google Scholar 

  4. C. G.Chehata (1958) On a theorem on ordered groups, Proc. Glasgow Math. Assoc. 4, 16–21.

    Google Scholar 

  5. A. H.Clifford (1952) A noncommutative ordinally simple linearly ordered group, Proc. Amer. Math. Soc. 2, 902–903.

    Google Scholar 

  6. M.Darnel (1987) Special-valued l-groups and abelian covers, Order 4, 191–194.

    Google Scholar 

  7. T.Feil (1980) A comparison of Chehata's and Clifford's ordinally simple ordered groups, Proc. Amer. Math. Soc. 79, 512–514.

    Google Scholar 

  8. T.Feil (1982) An uncountable tower of l-group varieties, Algebra Universalis 14, 129–131.

    Google Scholar 

  9. S. A. Gurchenkov and V. M. Kopytov (1987) On covers of the variety of abelian lattice-ordered groups (in Russian), Siberian Math. J. 28.

  10. H.Hollister (1972) Nilpotent l-groups are representable, Algebra Universalis 8, 65–71.

    Google Scholar 

  11. V. M. Kopytov, Nilpotent lattice-ordered groups, Sibirsk. Mat. Zh. 23, 127–131, 224.

    Google Scholar 

  12. N. Ya.Medvedev (1977) Varieties of lattice-ordered groups (Russian), Algebra i Logika 16, 40–45.

    Google Scholar 

  13. N. YaMedvedev (1984) Lattice of o-approximable l-varieties (Russian), Czech. Math. J. 34(109), 6–17.

    Google Scholar 

  14. N.Reilly (1983) Nilpotent, weakly abelian and Hamiltonian lattice-ordered groups, Czech. Math. J. 33(108), 348–353.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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Communicated by A. M. W. Glass

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Anderson, M., Darnel, M. & Feil, T. A variety of lattice-ordered groups containing all representable covers of the abelian variety. Order 7, 401–405 (1990). https://doi.org/10.1007/BF00383204

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  • DOI: https://doi.org/10.1007/BF00383204

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