Abstract
We prove a sufficient condition under which a semigroup admits no finite identity basis. As an application, it is shown that the identities of the Kauffman monoid \({\mathcal{K}_n}\) are nonfinitely based for each \({n \geq 3}\). This result holds also for the case when \({\mathcal{K}_n}\) is considered as an involution semigroup under either of its natural involutions.
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Presented by M. Jackson.
Dedicated to Brian Davey on the occasion of his 65th birthday
Yuzhu Chen, Xun Hu, Yanfeng Luo have been partially supported by the Natural Science Foundation of China (projects no. 10971086, 11371177). M. V. Volkov acknowledges support from the Presidential Programme “Leading Scientific Schools of the Russian Federation”, project no. 5161.2014.1, the Russian Foundation for Basic Research, project no. 14-01-00524, and the Ministry of Education and Science of the Russian Federation, project no. 1.1999.2014/K.
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Auinger, K., Chen, Y., Hu, X. et al. The finite basis problem for Kauffman monoids. Algebra Univers. 74, 333–350 (2015). https://doi.org/10.1007/s00012-015-0356-x
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DOI: https://doi.org/10.1007/s00012-015-0356-x