Journal of Mathematical Sciences

, Volume 131, Issue 6, pp 6023–6026 | Cite as

An Analogue of the Magnus Problem for Associative Algebras

  • V. Dotsenko
  • N. Iyudu
  • D. Korytin


We prove an analogue of the Magnus theorem for associative algebras without unity over arbitrary fields. Namely, if an algebra is given by n + k generators and k relations and has an n-element system of generators, then this algebra is a free algebra of rank n.


Associative Algebra Free Algebra Arbitrary Field 
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  1. 1.
    O. G. Kharlampovich, “Lyndon's condition for solvable Lie algebras,” Sov. Math., 28, No.9 (286), 50–59.Google Scholar
  2. 2.
    W. Magnus, “Uber freie Faktorgruppen und freie Untergruppen gegebener Gruppen,” Monatsh. Math. Phys., 47, 307–313 (1939).CrossRefGoogle Scholar
  3. 3.
    W. Magnus, A. Karrass, and D. Solitar, Combinatorial Group Theory: Presentation of Groups in Terms of Generators and Relations, Wiley, New York (1966).Google Scholar
  4. 4.
    I. S. Romanovskii, “Free subgroups infinitely presented groups,” Algebra Logika, 16, 62–68 (1978).CrossRefGoogle Scholar
  5. 5.
    L. M. Shneerson, “On free subsemigroups infinitely presented semigroups,” Sib. Mat. Zh., 15, 325–328 (1974).CrossRefGoogle Scholar
  6. 6.
    L. M. Shneerson, “On free subalgebras of finitely presented algebras,” in: Proc. IV USSR Symp. Theory of Rings, Algebras, and Modules [in Russian], Kishinev (1980), pp. 117–118.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • V. Dotsenko
    • 1
    • 2
  • N. Iyudu
    • 1
  • D. Korytin
    • 1
  1. 1.Moscow State UniversityMoscowRussia
  2. 2.Independent University of MoscowMoscowRussia

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