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A note on maximal regular subsemigroups of the finite transformation semigroups \(\mathcal{T}(n,r)\)

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Abstract

Let \(\mathcal{T}_{n}\) be the semigroup of all full transformations on the finite set X n ={1,2,…,n}. For 1≤r≤n, set \(\mathcal {T}(n, r)=\{ \alpha\in\mathcal{T}_{n} | \operatorname{rank}(\alpha)\leq r\}\). In this note we show that, for 2≤r≤n−2, any maximal regular subsemigroup of the semigroup \(\mathcal{T} (n,r)\) is idempotent generated, but this may not happen in the semigroup \(\mathcal{T}(n, n-1)\).

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Acknowledgements

The authors would like to thank the referee for his/her valuable suggestions and comments which help to improve the presentation of this note.

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Authors and Affiliations

  1. School of Mathematics and Computer Sciences, Guizhou Normal University, Guiyang, GuiZhou Province, 550001, P.R. China

    Ping Zhao & Taijie You

  2. Mathematics Teaching & Research Section, Guiyang Medical College, Guiyang, GuiZhou Province, 550004, P.R. China

    Ping Zhao

  3. Department of Biomedical Engineering, Guiyang Medical College, Guiyang, GuiZhou Province, 550004, P.R. China

    Huabi Hu

Authors
  1. Ping Zhao
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  2. Huabi Hu
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  3. Taijie You
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Corresponding author

Correspondence to Huabi Hu.

Additional information

Communicated by Jean-Eric Pin.

This work is supported by Natural Science Fund of Guizhou (No. [2013]2225).

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Zhao, P., Hu, H. & You, T. A note on maximal regular subsemigroups of the finite transformation semigroups \(\mathcal{T}(n,r)\) . Semigroup Forum 88, 324–332 (2014). https://doi.org/10.1007/s00233-013-9523-6

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  • DOI: https://doi.org/10.1007/s00233-013-9523-6

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