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On Varieties Generated by Minimal Complex Semigroups

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Abstract

A semigroup is complex if it generates a variety the subvariety lattice of which contains an isomorphic copy of every finite lattice. It is known that a complex semigroup has at least four elements and that up to isomorphism and anti-isomorphism, there are four complex semigroups of order four. Subvarieties of the varieties generated by two of these four minimal complex semigroups have previously been described. To complete the study, we describe subvarieties of the varieties generated by the remaining two semigroups.

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Authors and Affiliations

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

    Wen Ting Zhang & Yan Feng Luo

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  1. Wen Ting Zhang
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  2. Yan Feng Luo
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Correspondence to Yan Feng Luo.

Additional information

This research was partially supported by the National Natural Science Foundation of China (No.10571077) and the Natural Science Foundation of Gansu Province (No.3ZS052-A25-017)

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Zhang, W.T., Luo, Y.F. On Varieties Generated by Minimal Complex Semigroups . Order 25, 243–266 (2008). https://doi.org/10.1007/s11083-008-9092-6

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  • DOI: https://doi.org/10.1007/s11083-008-9092-6

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