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 identities. 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

^ R. Padmanabhan, Axioms for Lattices and Boolean Algebras, World Scientific Publishing Company (2008)
^ Jónsson, Bjarni (1967). "Algebras Whose Congruence Lattices Are Distributive". Mathematica Scandinavica. 21 (1): 110–121. doi:10.7146/math.scand.a-10850. JSTOR 24489650.
^ Clifford Bergman, Universal Algebra: Fundamentals and Selected Topics, Taylor & Francis (2011), p. 124 - 126

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