Abstract
Three finite involution semigroups sharing a common semigroup reduct are constructed so that one has a finite identity basis, one has an infinite irredundant identity basis, and one has no irredundant identity bases. Then an infinite class of finite involution semigroups is exhibited with the property that as involution semigroups, the varieties they generate constitute two incomparable infinite chains, while as semigroups, the varieties they generate constitute a single infinite chain.
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References
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Lee, E.W.H. (2023). Counterintuitive Examples of Involution Semigroups. In: Advances in the Theory of Varieties of Semigroups. Frontiers in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-16497-2_9
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DOI: https://doi.org/10.1007/978-3-031-16497-2_9
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