Mathematical Notes

, Volume 73, Issue 3–4, pp 474–481 | Cite as

Identities of Semigroups of Triangular Matrices over Finite Fields

  • M. V. Volkov
  • I. A. Gol'dberg


It is proved that the semigroup of all triangular n × n matrices over a finite field K is inherently nonfinitely based if and only if n > 3 and |K|> 2.

finite semigroup finite base property finite field locally finite variety inherently nonfinitely based variety semigroup of triangular matrices 


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  1. 1.
    S. Oates and M. B. owell, “Identical relations in finite groups,” J. Algebra, 1 (1964), no. 1, 11–39.Google Scholar
  2. 2.
    P. Perkins, “Bases for equational theories of semigroups,” J. Algebra, 11 (1969), no. 2, 298–314.Google Scholar
  3. 3.
    L. N. Shevrin and M. V. Volkov, “Identities of semigroups,” Izv. Vyssh. Uchebn. Zaved. Mat. [Soviet Math. (Iz. VUZ)], (1985), no. 11, 3–47.Google Scholar
  4. 4.
    M. V. Volkov, “The finite basis problem for finite semigroups,” Sci. Math. Jpn., 53 (2001), no. 1, 171–199.Google Scholar
  5. 5.
    A. I. Mal'tsev, Algebraic Systems [in Russian], Nauka, Moscow, 1970; English translation in: A. I. Malcev, Algebraic Systems, Die Grundlehren der mathematischen Wissenschaften, Band 192, Springer-Verlag, New York–Heidelberg, 1973.Google Scholar
  6. 6.
    M. V. Sapir, “Problems of Burnside type and the finite basis property in varieties of semigroups,” Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.], 51 (1987), no. 2, 319–340.Google Scholar
  7. 7.
    A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups, vol. I, II, Mathematical Surveys, no. 7, American Mathematical Society, Providence, RI, 1961, 1967.Google Scholar
  8. 8.
    L. N. Shevrin, “On the theory of epigroups. I,” Mat. Sb. [Russian Acad. Sci. Sb. Math.], 185 (1994), no. 8, 129–160.Google Scholar
  9. 9.
    M. V. Sapir, “Inherently non-finitely based finite semigroups,” Mat. Sb. [Math. USSR-Sb.], 133 (1987), no. 2, 154–166.Google Scholar
  10. 10.
    M. Jackson, “Small inherently nonfinitely based finite semigroups,” Semigroup Forum (to appear).Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • M. V. Volkov
    • 1
  • I. A. Gol'dberg
    • 1
  1. 1.Ekaterinburg Ural State UniversityRussia

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