universal algebra Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures in general, not specific types of algebraic structures. For instance, rather than considering groups or rings as the object of stud ...

, within

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

, a majority term, sometimes called a Jónsson term, is a term ''t'' with exactly three

free variable In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a variable may be said to be either free or bound. Some older books use the terms real variable and apparent variable for f ...

s that satisfies the

equation In mathematics, an equation is a mathematical 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 ...

s ''t''(''x'', ''x'', ''y'') = ''t''(''x'', ''y'', ''x'') = ''t''(''y'', ''x'', ''x'') = ''x''. For example, for

lattice Lattice may refer to: Arts and design * Latticework, an ornamental criss-crossed framework, an arrangement of crossing laths or other thin strips of material * Lattice (music), an organized grid model of pitch ratios * Lattice (pastry), an or ...

s, 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 Variety may refer to: Arts and entertainment Entertainment formats * Variety (radio) * Variety show, in theater and television Films * ''Variety'' (1925 film), a German silent film directed by Ewald Andre Dupont * ''Variety'' (1935 film), ...

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 A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

Bjarni Jónsson Bjarni Jónsson (February 15, 1920 – September 30, 2016) was an Icelandic mathematician and logician working in universal algebra, lattice theory, model theory and set theory. He was emeritus distinguished professor of mathematics at Vanderb ...

References

{{reflist Universal algebra