Mathematical Notes

, Volume 63, Issue 5, pp 569–574 | Cite as

Varieties of solvable Lie rings of finite width

  • D. S. Ananichev
  • M. V. Volkov


A complete description of the varieties of Lie rings whose lattice of subvarieties has finite width is obtained.

Key words

variety of rings solvable ring ordered set width of a variety finite ring locally finite variety Cross variety Engel variety 


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  1. 1.
    V. A. Artamonov, “Chain varieties of linear algebras,”Trudy Moskov. Mat. Obshch. [Trans. Moscow Math. Soc.],29, 51–78 (1973).MATHMathSciNetGoogle Scholar
  2. 2.
    V. A. Artamonov, “Lattices of varieties of linear algebras,”Uspekhi Mat. Nauk [Russian Math. Surveys],33, No. 2, 135–167 (1978).MATHMathSciNetGoogle Scholar
  3. 3.
    D. S. Ananichev, “Almost distributive varieties of Lie rings,”Mat. Sb. [Russian Acad. Sci. Sb. Math.],186, No. 4, 3–20 (1995).MATHMathSciNetGoogle Scholar
  4. 4.
    R. P. Dilworth, “A decomposition theorem for partially ordered sets,”Ann. of Math.,51, No. 1, 161–166 (1950).MATHMathSciNetGoogle Scholar
  5. 5.
    M. V. Volkov and A. G. Gein, “Identities of almost nilpotent Lie rings,”Mat. Sb. [Math. USSR-Sb.],118, No. 1, 132–142 (1982).MathSciNetGoogle Scholar
  6. 6.
    I. V. L'vov, “Varieties of associative rings. I,”Algebra i Logika [Algebra and Logic],12, No. 3, 269–297 (1973).MATHMathSciNetGoogle Scholar
  7. 7.
    Yu. A. Bakhturin and A. Yu. Ol'shanskii, “Identical relations in finite Lie rings,”Mat. Sb. [Math. USSR-Sb.],96, No. 4., 543–559 (1975).MathSciNetGoogle Scholar
  8. 8.
    Yu. A. Bakhturin,Identities in Lie Algebras [in Russian], Nauka, Moscow (1985).Google Scholar
  9. 9.
    Yu. A. Bakhturin and A. Yu. Ol'shanskii, “Solvable almost Cross varieties of Lie rings,”Mat. Sb. [Math. USSR-Sb.],100, No. 3, 384–399 (1976).MathSciNetGoogle Scholar
  10. 10.
    G. Birkhoff,Lattice Theory Colloquium Publications, Amer. Math. Soc. Princeton, N.J. (1948)Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • D. S. Ananichev
    • 1
  • M. V. Volkov
    • 1
  1. 1.Ural State UniversityEkaterinburg

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