algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary a ...

, ''n''-ary associativity is a

generalization A generalization is a form of abstraction whereby common properties of specific instances are formulated as general concepts or claims. Generalizations posit the existence of a domain or set of elements, as well as one or more common characteri ...

of the

associative law In mathematics, the associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement f ...

to ''n''-ary operations. Ternary associativity is : (''abc'')''de'' = ''a''(''bcd'')''e'' = ''ab''(''cde''), i.e. the string ''abcde'' with any three adjacent elements bracketed. ''n''-ary associativity is a string of length ''n'' + (''n'' − 1) with any ''n'' adjacent elements bracketed..

References

Properties of binary operations {{algebra-stub