Abstract
A monoid is pseudo-complex if the semigroup variety it generates has uncountably many subvarieties, while the monoid variety it generates has only finitely many subvarieties. The smallest pseudo-complex monoid currently known is of order seven. The present article exhibits a pseudo-complex monoid of order six and shows that every smaller monoid is not pseudo-complex. Consequently, minimal pseudo-complex monoids are of order six.
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Acknowledgements
The author is indebted to the reviewer for a number of important suggestions. He is also grateful to Sergey Gusev, Marcel Jackson, and Boris Vernikov for many fruitful discussions on monoid varieties.
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In memory of Professor Mark V. Sapir (1957–2022).
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Lee, E.W.H. A minimal pseudo-complex monoid. Arch. Math. 120, 15–25 (2023). https://doi.org/10.1007/s00013-022-01797-z
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DOI: https://doi.org/10.1007/s00013-022-01797-z