Algebra universalis

, Volume 74, Issue 3–4, pp 333–350 | Cite as

The finite basis problem for Kauffman monoids

  • K. Auinger
  • Yuzhu Chen
  • Xun Hu
  • Yanfeng Luo
  • M. V. Volkov


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.

Key words and phrases

semigroup involution semigroup semigroup identity variety finite basis problem Kauffman monoid wire monoid Rees matrix semigroup 

2010 Mathematics Subject Classification

Primary: 20M07 


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© Springer Basel 2015

Authors and Affiliations

  • K. Auinger
    • 1
  • Yuzhu Chen
    • 2
    • 3
  • Xun Hu
    • 2
    • 3
    • 4
  • Yanfeng Luo
    • 2
    • 3
  • M. V. Volkov
    • 5
  1. 1.Fakultät für MathematikUniversität WienWienAustria
  2. 2.Department of Mathematics and StatisticsLanzhou UniversityLanzhouChina
  3. 3.Key Laboratory of Applied Mathematics and Complex SystemsGansu ProvinceChina
  4. 4.Department of Mathematics and StatisticsChongqing Technology and Business UniversityChongqingChina
  5. 5.Institute of Mathematics and Computer ScienceUral Federal UniversityEkaterinburgRussia

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