A nonfinitely based semigroup of triangular matrices

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Abstract

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.

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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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