A Nonfinitely Based Semigroup of Triangular Matrices

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 142)

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 \(\mathrm {UT}_3(\mathbb {R})\) of all upper triangular real \(3\times 3\)-matrices with 0 s and/or 1 s on the main diagonal. The result holds also for the case when \(\mathrm {UT}_3(\mathbb {R})\) is considered as an involution semigroup under the reflection with respect to the secondary diagonal.

Keywords

Semigroup reduct Involution semigroup semigroup variety 

Notes

Acknowledgments

The author gratefully acknowledges support from the Presidential Programme “Leading Scientific Schools of the Russian Federation”, project no. 5161.2014.1, and from the Russian Foundation for Basic Research, project no. 14-01-00524. In particular, the latter project was used to support the author’s participation in the International Conference on Semigroups, Algebras and Operator Theory (ICSAOT-2014) held at the Cochin University of Science and Technology as well as his participation in the International Conference on Algebra and Discrete Mathematics (ICADM-2014) held at Government College, Kattappana. Also the author expresses cordial thanks to the organizers of these two conferences, especially to Dr. P. G. Romeo, Convenor of ICSAOT-2014, and Sri. G. N. Prakash, Convenor of ICADM-2014, for their warm hospitality.

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Copyright information

© Springer India 2015

Authors and Affiliations

  1. 1.Institute of Mathematics and Computer ScienceUral Federal UniversityEkaterinburgRussia

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