Congruence modularity implies cyclic terms for finite algebras

Abstract

An n-ary operation f on a set A is called cyclic if it is idempotent and f(a_1, a_2, a_3, ..., a_n) = f(a_2, a_3, ..., a_n, a_1) for every a_1, ... 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|.

Keywords

• Congruence
• modularity
• implies
• cyclic
• terms
• finite
• algebras