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  • ON THE VARIETY GENERATED BY THE MONOID OF TRIANGULAR 2×2 MATRICES OVER A TWO-ELEMENT FIELD

  • Part of
  • WEN TING ZHANG, JIAN RONG LI, YAN FENG LUO
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 86 / Issue 1 / August 2012
    Published online by Cambridge University Press:
    28 May 2012, pp. 64-77
    Print publication:
    August 2012
    • Article
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  • Let 𝒯n(F) denote the monoid of all upper triangular n×n matrices over a finite field F. It has been shown by Volkov and Goldberg that 𝒯n(F) is nonfinitely based if ∣F∣>2 and n≥4, but the cases when ∣F∣>2 and n=2,3 or when ∣F∣=2 have remained open. In this paper, it is shown that the monoid 𝒯2 (F) is finitely based when ∣F∣=2 , and a finite identity basis for it is given. Moreover, all maximal subvarieties of the variety generated by 𝒯2 (F) with ∣F∣=2 are determined.