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Minimal non-finitely based semigroups

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Abstract

This is an announcement of the complete identification, up to isomorphism, of all semigroups that are minimal with respect to being non-finitely based.

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Notes

  1. Note that the zero element 0 of the semigroup A 2 is no longer a zero element in the semigroup \(A_{2}^{g}\).

  2. An explicit basis for the semigroup \(A_{2}^{g}\) can be found in Lee and Volkov [7] and Volkov et al. [22].

  3. A generalization of this result can be found in Lee [5].

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Acknowledgements

The authors are indebted to Professor Mikhail V. Volkov for advice and a number of very useful suggestions.

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Authors and Affiliations

  1. Division of Math, Science, and Technology, Nova Southeastern University, Fort Lauderdale, FL, 33314, USA

    Edmond W. H. Lee

  2. Department of Mathematics, Lanzhou University, Lanzhou, Gansu, 730000, P.R. China

    Jian Rong Li & Wen Ting Zhang

Authors
  1. Edmond W. H. Lee
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  2. Jian Rong Li
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  3. Wen Ting Zhang
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Corresponding author

Correspondence to Wen Ting Zhang.

Additional information

Communicated by Mikhail V. Volkov.

The second and third authors were partially supported by the National Natural Science Foundation of China (No. 10971086), the Mathematical Tianyuan Foundation of China (No. 11126186), 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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Lee, E.W.H., Li, J.R. & Zhang, W.T. Minimal non-finitely based semigroups. Semigroup Forum 85, 577–580 (2012). https://doi.org/10.1007/s00233-012-9434-y

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