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.

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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