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