Skip to main content
SpringerLink
Log in

Theory of varieties of lattice ordered groups

  • Published:
Algebra and Logic Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Literature cited

  1. J. Martinez, "Free products in varieties of lattice ordered groups," Czech. Math. J.,22, No. 4, 535–553 (1972).

    Google Scholar 

  2. E. B. Scrimger, "A large class of small varieties of lattice-ordered groups," Proc. Am. Math. Soc.,51, No. 2, 301–306 (1975).

    Google Scholar 

  3. C. D. Fix, "On the Scrimger varieties of lattice ordered groups," Algebra Univ.,16, No. 2, 163–166 (1983).

    Google Scholar 

  4. S. A. Gurchenkov, "Varieties of ℓ-groups with the identity [xp, yp] = e are finitely based," Algebra Logika,23, No. 1, 27–47 (1984).

    Google Scholar 

  5. W. C. Holland, A. H. Mekler, and N. R. Reily, "Varieties of lattice ordered groups in which prime powers commute," Preprint (1984).

  6. S. A. Gurchenkov, "On varieties of ℓ-groups in which linearly ordered groups are Abelian," 20th All-Union Symp. on Group Theory, Gomel (1986), p. 69.

  7. S. A. Gurchenkov, "On the finite basis property of certain ℓ-varieties," 9th All-Union Symp. on Group Theory, Moscow (1984), p. 194.

  8. N. R. Reily, "Varieties of lattice ordered groups that contain no non-Abelian o-groups are solvable," Abstr. Am. Math. Sic.,7, No. 2, 223 (1986).

    Google Scholar 

  9. V. M. Kopytov and N. Ya. Medvedev, "On varieties of lattice ordered groups," Algebra Logika,16, No. 4, 417–423 (1977).

    Google Scholar 

  10. T. Feil, "An uncountable tower of ℓ-group varieties," Algebra Univ.,14, No. 1, 129–131 (1982).

    Google Scholar 

  11. N. Ya. Medvedev, "ℓ-varieties without an independent basis of identities," Math. Slovaca,32, No. 4, 417–425 (1982).

    Google Scholar 

  12. N. Ya. Medvedev, "On coverings in a lattice of ℓ-varieties," Algebra Logika,22, No. 1, 53–60 (1983).

    Google Scholar 

  13. S. A. Gurchenkov, "On varieties of nilpotent lattice ordered groups," Algebra Logika,21, No. 5, 499–510 (1982).

    Google Scholar 

  14. S. A. Gurchenkov, "On varieties of ℓ-groups with infinite axiomatic rank," Sib. Mat. Zh.,26, No. 1, 66–70 (1985).

    Google Scholar 

  15. V. M. Kopytov, Lattice Ordered Groups [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  16. M. I. Kargapolov and Yu. I. Merzlyakov, Foundations of Group Theory [in Russian], 3rd ed., Nauka, Moscow (1982).

    Google Scholar 

  17. S. A. Gurchenkov, "On coverings in a lattice of ℓ-varieties," Mat. Zametki,35, No. 5, 677–684 (1984).

    Google Scholar 

  18. S. A. Gurchenkov and V. M. Kopytov, "On a description of coverings of the variety of Abelian lattice ordered groups," Sib. Mat. Zh.,28, No. 3, 66–69 (1987).

    Google Scholar 

  19. K. A. Baker, "Primitive satisfaction and equational problems for lattices and other algebras," Trans. Am. Math. Soc.,190, No. 1, 125–150 (1974).

    Google Scholar 

Download references

Authors
  1. S. A. Gurchenkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Algebra i Logika, Vol. 27, No. 3, pp. 249–273, May–June, 1988.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gurchenkov, S.A. Theory of varieties of lattice ordered groups. Algebra and Logic 27, 153–167 (1988). https://doi.org/10.1007/BF01978561

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01978561

Keywords

Search

Navigation