Algebra universalis

, 61:365 | Cite as

Congruence modularity implies cyclic terms for finite algebras

  • Libor Barto
  • Marcin Kozik
  • Miklós Maróti
  • Ralph McKenzie
  • Todd Niven


An n-ary operation f : A n A is called cyclic if it is idempotent and \({f(a_1, a_2, a_3, \ldots , a_n) = f(a_2, a_3, \ldots , a_n, a_1)}\) for every \({a_1, \ldots, a_n \in A}\). We prove that every finite algebra A in a congruence modular variety has a p-ary cyclic term operation for any prime p greater than |A|.

2000 Mathematics Subject Classification

Primary: 08B10 Secondary: 08B05 

Key words and phrases

Maltsev condition cyclic term congruence modularity weak near-unanimity 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • Libor Barto
    • 1
  • Marcin Kozik
    • 2
    • 3
  • Miklós Maróti
    • 4
  • Ralph McKenzie
    • 5
  • Todd Niven
    • 3
  1. 1.Department of AlgebraCharles UniversityPragueCzech Republic
  2. 2.Department of Theoretical Computer ScienceJagiellonian UniversityKrakowPoland
  3. 3.Eduard Čech CenterPragueCzech Republic
  4. 4.Bolyai Institute, University of SzegedSzegedHungary
  5. 5.Department of MathematicsVanderbilt UniversityNashvilleUSA

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