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Jónsson Term
In universal algebra, within mathematics, a majority term, sometimes called a Jónsson term, is a term (logic), term ''t'' with exactly three free variables that satisfies the equations ''t''(''x'', ''x'', ''y'') = ''t''(''x'', ''y'', ''x'') = ''t''(''y'', ''x'', ''x'') = ''x''. For example, for lattice (order), 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 conditions, Maltsev condition, a Variety (universal algebra), 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 nam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Universal Algebra
Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures. For instance, rather than take particular groups as the object of study, in universal algebra one takes the class of groups as an object of study. Basic idea In universal algebra, an algebra (or algebraic structure) is a set ''A'' together with a collection of operations on ''A''. An ''n''- ary operation on ''A'' is a function that takes ''n'' elements of ''A'' and returns a single element of ''A''. Thus, a 0-ary operation (or ''nullary operation'') can be represented simply as an element of ''A'', or a '' constant'', often denoted by a letter like ''a''. A 1-ary operation (or ''unary operation'') is simply a function from ''A'' to ''A'', often denoted by a symbol placed in front of its argument, like ~''x''. A 2-ary operation (or ''binary operation'') is often denoted by a symbol placed between its argum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |