In
universal algebra, within
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, a majority term, sometimes called a Jónsson term, is a
term ''t'' with exactly three
free variables that satisfies the
equation
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for example, in ...
s ''t''(''x'', ''x'', ''y'') = ''t''(''x'', ''y'', ''x'') = ''t''(''y'', ''x'', ''x'') = ''x''.
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.
The case of a majority term is given by the special case ''n=2'' of a sequence of Jónsson terms.
[Clifford Bergman, Universal Algebra: Fundamentals and Selected Topics, Taylor & Francis (2011), p. 124 - 126]
Jónsson terms are named after the Icelandic
mathematician Bjarni Jónsson.
References
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Universal algebra