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Hereditarily Finitely Based Semigroups of Triangular Matrices over Finite Fields

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Abstract

Denote by the semigroup of all n×n upper triangular matrices over the field F q of order q. It is shown that the variety generated by is hereditarily finitely based if and only if n≤2. Moreover, the semigroup is not hereditarily finitely based for any n≥3 and any q≥2.

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Notes

  1. Here and below, when specifying a substitution, we always assume that it fixes all letters except those explicitly mentioned.

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Acknowledgements

The authors would like to express their gratitude to Dr E.W.H. Lee for his comments and help in checking and revising the article, and also to the referees for their valuable remarks and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Lanzhou University, Lanzhou, Gansu, 730000, People’s Republic of China

    Wen Ting Zhang, Jian Rong Li & Yan Feng Luo

Authors
  1. Wen Ting Zhang
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  2. Jian Rong Li
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  3. Yan Feng Luo
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Corresponding author

Correspondence to Wen Ting Zhang.

Additional information

Communicated by Mikhail Volkov.

This research was partially supported by the National Natural Science Foundation of China (No. 10971086), the Natural Science Foundation of Gansu Province (No. 1107RJZA218), and the Fundamental Research Funds for the Central Universities (No. lzujbky-2012-12).

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Zhang, W.T., Li, J.R. & Luo, Y.F. Hereditarily Finitely Based Semigroups of Triangular Matrices over Finite Fields. Semigroup Forum 86, 229–261 (2013). https://doi.org/10.1007/s00233-013-9476-9

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  • DOI: https://doi.org/10.1007/s00233-013-9476-9

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