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

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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

Full-text PDF (201 kB) Citations (10)

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DOI: https://doi.org/10.4213/mzm210

Abstract: It is proved that the semigroup of all triangular

$n\times n$ 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:

E. W. H. Lee, “On the intersection of finitely generated varieties of monoids”, UMN, 80:2(482) (2025), 165–166
Edmond W. H. Lee, Frontiers in Mathematics, Advances in the Theory of Varieties of Semigroups, 2023, 1
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
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
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
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
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
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
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
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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