Geodesic
Identities of Semigroups of Triangular Matrices over Finite Fields
Matematičeskie zametki, Tome 73 (2003) no. 4, pp. 502-510

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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 $|K|> 2$. 
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     author = {M. V. Volkov and I. A. Gol'dberg},
     title = {Identities of {Semigroups} of {Triangular} {Matrices} over {Finite} {Fields}},
     journal = {Matemati\v{c}eskie zametki},
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M. V. Volkov; I. A. Gol'dberg. Identities of Semigroups of Triangular Matrices over Finite Fields. Matematičeskie zametki, Tome 73 (2003) no. 4, pp. 502-510. http://geodesic.mathdoc.fr/item/MZM_2003_73_4_a2/