Korean J. Math. Vol. 27 No. 1 (2019) pp.53-62
DOI: https://doi.org/10.11568/kjm.2019.27.1.53

Non-finitely based finite involution semigroups with finitely based semigroup reducts

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Published: Mar 30, 2019
Keywords:
Semigroup, involution, finitely based, finite basis problem
Mathematics Subject Classification:
20M05

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Edmond W. H. Lee
Department of Mathematics, Nova Southeastern University, Fort Lauderdale, FL 33314, USA

Abstract

Recently, an infinite class of finitely based finite involution semigroups with non-finitely based semigroup reducts have been found. In contrast, only one example of the opposite type---non-finitely based finite involution semigroups with finitely based semigroup reducts---has so far been published. In the present article, a sufficient condition is established under which an involution semigroup is non-finitely based. This result is then applied to exhibit several examples of the desired opposite type.


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