Algebra universalis

, Volume 61, Issue 3, pp 365-380

Congruence modularity implies cyclic terms for finite algebras

  • Libor BartoAffiliated withDepartment of Algebra, Charles University Email author 
  • , Marcin KozikAffiliated withDepartment of Theoretical Computer Science, Jagiellonian UniversityEduard Čech Center
  • , Miklós MarótiAffiliated withBolyai Institute, University of Szeged
  • , Ralph McKenzieAffiliated withDepartment of Mathematics, Vanderbilt University
  • , Todd NivenAffiliated withEduard Čech Center

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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