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Existence of a new limit variety of aperiodic monoids

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Abstract

Presently, the two limit varieties of Marcel Jackson are the only known examples of limit varieties of aperiodic monoids. This article establishes the existence of a new example by showing that a certain aperiodic monoid of order seven is non-finitely based. This monoid turns out to be a smallest non-finitely based monoid that is not inherently non-finitely based.

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Acknowledgements

The author is grateful to the following people: the anonymous referee for a thorough review, Marcel Jackson for suggestions that substantially simplified some arguments, and Edmond W. H. Lee for suggesting the investigation of the monoid L 1 and for help in revising this article.

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Authors and Affiliations

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

    Wen Ting Zhang

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  1. Wen Ting Zhang
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Correspondence to Wen Ting Zhang.

Additional information

Communicated by Marcel Jackson.

This research was 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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Zhang, W.T. Existence of a new limit variety of aperiodic monoids. Semigroup Forum 86, 212–220 (2013). https://doi.org/10.1007/s00233-012-9410-6

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  • DOI: https://doi.org/10.1007/s00233-012-9410-6

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