A nonfinitely based semigroup of triangular matrices

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.