Jónsson term

In universal algebra, within mathematics, a majority term, sometimes called a Jónsson term, is a term t with exactly three free variables that satisfies the equations t(x, x, y) = t(x, y, x) = t(y, x, x) = x.[1]

For example for lattices, the term (x ∧ y) ∨ (y ∧ z) ∨ (z ∧ x) is a Jónsson term.

Sequences of Jónsson term

In general, Jónsson terms, more formally, a sequence of Jónsson terms, is a sequence of ternary terms satisfying certain related idenitities. One of the earliest Maltsev condition, a variety is congruence distributive if and only if it has a sequence of Jónsson terms. [2]

The case of a majority term is given by the special case n=2 of a sequence of Jónsson terms. [3]

Jónsson terms are named after the Icelandic mathematician Bjarni Jónsson.

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References
  1. R. Padmanabhan, Axioms for Lattices and Boolean Algebras, World Scientific Publishing Company (2008)
  2. Originally proved in B. Jónsson, Algebras whose congruence lattices are distributive. Math. Scand., 21:110-121, 1967.
  3. Clifford Bergman, Universal Algebra: Fundamentals and Selected Topics, Taylor & Francis (2011), p. 124 - 1256
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