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All idempotent hypersubstitutions of type (2,2)

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Abstract

A hypersubstitution of type (2,2) is a map σ which takes the binary operation symbols f and g to binary terms σ(f) and σ(g). Any such σ can be inductively extended to a map \(\hat{\sigma}\) on the set of all terms of type (2,2). By using this extension on the set Hyp(2,2) of all hypersubstitutions of type (2,2) a binary operation can be defined. Together with the identity hypersubstitution mapping f to f(x 1,x 2) and g to g(x 1,x 2) the set Hyp(2,2) forms a monoid. This monoid is isomorphic to the endomorphism monoid of the clone of all binary terms of type (2,2). We determine all idempotent elements of this monoid. The results can be applied to the equational theory of Universal Algebra.

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References

  1. Denecke, K., Koppitz, J.: Finite Monoids of Hypersubstitutions of Type τ=(2). Semigroup Forum 56, 265–275 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  2. Denecke, K., Wismath, S.L.: The Monoid of Hypersubstitutions of type (2). Contributions to General Algebra, 10. In: Proceedings of the Klagenfurt Conference 1997, May 29–June 1, pp. 109–126. Johannes Heyn, Klagenfurt (1998)

    Google Scholar 

  3. Denecke, K., Wismath, S.L.: Hyperidentities and Clones. Gordon and Breach, London (2000)

    MATH  Google Scholar 

  4. Denecke, K., Lau, D., Pöschel, R., Schweigert, D.: Hypersubstitutions, hyperequational classes and clone congruences. Contrib. Gen. Algebra 7, 97–118 (1991)

    Google Scholar 

  5. Denecke, K., Jampachon, P., Wismath, S.L.: Clones of n-ary algebras. J. Appl. Algebra Discrete Math. 1(2), 141–158 (2003)

    MATH  MathSciNet  Google Scholar 

  6. Menger, K.: The algebra of functions: past, present, future. Rend. Math. 20, 409–430 (1961)

    MATH  MathSciNet  Google Scholar 

  7. Wismath, S.L.: The monoid of hypersubstitutions of type (n). Southeast Asian Bull. Math. 24, 115–128 (2000)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, KhonKaen University, KhonKaen, Thailand

    Tawat Cangpas

  2. Institut für Mathematik, Universität Potsdam, PF 601553, 14415, Potsdam, Germany

    Klaus Denecke

Authors
  1. Tawat Cangpas
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  2. Klaus Denecke
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Correspondence to Klaus Denecke.

Additional information

Communicated by Mikhail Volkov.

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Cangpas, T., Denecke, K. All idempotent hypersubstitutions of type (2,2). Semigroup Forum 76, 525–539 (2008). https://doi.org/10.1007/s00233-008-9048-6

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  • DOI: https://doi.org/10.1007/s00233-008-9048-6

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