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Matematicheskie Zametki, 2003, Volume 73, Issue 4, Pages 502–510
DOI: https://doi.org/10.4213/mzm210
(Mi mzm210)
 

This article is cited in 10 scientific papers (total in 10 papers)

Identities of Semigroups of Triangular Matrices over Finite Fields

M. V. Volkov, I. A. Gol'dberg

Ural State University
References:
Abstract: 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.
Received: 17.10.2001
English version:
Mathematical Notes, 2003, Volume 73, Issue 4, Pages 474–481
DOI: https://doi.org/10.1023/A:1023298919061
Bibliographic databases:
UDC: 512.532.2
Language: Russian
Citation: M. V. Volkov, I. A. Gol'dberg, “Identities of Semigroups of Triangular Matrices over Finite Fields”, Mat. Zametki, 73:4 (2003), 502–510; Math. Notes, 73:4 (2003), 474–481
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/mzm210
  • https://doi.org/10.4213/mzm210
  • https://www.mathnet.ru/eng/mzm/v73/i4/p502
  • This publication is cited in the following 10 articles:
    1. E. W. H. Lee, “On the intersection of finitely generated varieties of monoids”, UMN, 80:2(482) (2025), 165–166  mathnet  crossref
    2. Edmond W. H. Lee, Frontiers in Mathematics, Advances in the Theory of Varieties of Semigroups, 2023, 1  crossref
    3. João Araújo, João Pedro Araújo, Peter J. Cameron, Edmond W.H. Lee, Jorge Raminhos, “A survey on varieties generated by small semigroups and a companion website”, Journal of Algebra, 635 (2023), 698  crossref
    4. Zhang W.T., Luo Ya.F., “The Finite Basis Problem For Involution Semigroups of Triangular \$2\Times 2\$ Matrices”, Bull. Aust. Math. Soc., 101:1 (2020), 88–104  crossref  mathscinet  isi  scopus
    5. Wen Ting Zhang, Ying Dan Ji, Yan Feng Luo, “The finite basis problem for infinite involution semigroups of triangular 2 $\times $ × 2 matrices”, Semigroup Forum, 94:2 (2017), 426  crossref
    6. Chen Yu., Hu X., Luo Ya., “The finite basis property of a certain semigroup of upper triangular matrices over a field”, J. Algebra. Appl., 15:9 (2016), 1650177  crossref  mathscinet  zmath  isi  elib  scopus
    7. Auinger K., Dolinka I., Pervukhina T.V., Volkov M.V., “Unary Enhancements of Inherently Non-Finitely Based Semigroups”, Semigr. Forum, 89:1 (2014), 41–51  crossref  mathscinet  zmath  isi  scopus  scopus
    8. Zhang W.T., Li J.R., Luo Ya.F., “Hereditarily Finitely Based Semigroups of Triangular Matrices Over Finite Fields”, Semigr. Forum, 86:2 (2013), 229–261  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    9. Zhang W.T., Li J.R., Luo Ya.F., “On the Variety Generated by the Monoid of Triangular 2 X 2 Matrices Over a Two-Element Field”, Bull. Aust. Math. Soc., 86:1 (2012), 64–77  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    10. Almeida J., Margolis S. W., Volkov M. V., “The pseudovariety of semigroups of triangular matrices over a finite field”, Theor. Inform. Appl., 39:1 (2005), 31–48  crossref  mathscinet  zmath  isi  scopus  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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