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.
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
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