A new sufficient condition under which a semigroup admits no finite identity basis has been recently suggested in a joint paper by Karl Auinger, Yuzhu Chen, Xun Hu, Yanfeng Luo, and the author. Here we apply this condition to show the absence of a finite identity basis for the semigroup UT3(ℝ) of all upper triangular real 3×3-matrices with 0 s and/or 1 s on the main diagonal. The result holds also for the case when UT3(ℝ) is considered as an involution semigroup under the reflection with respect to the secondary diagonal.
CITATION STYLE
Volkov, M. V. (2015). A nonfinitely based semigroup of triangular matrices. In Springer Proceedings in Mathematics and Statistics (Vol. 142, pp. 27–38). Springer New York LLC. https://doi.org/10.1007/978-81-322-2488-4_2
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