N-ary associativity explained

In algebra, -ary associativity is a generalization of the associative law to -ary operations.

A ternary operation is ternary associative if one has always

that is, the operation gives the same result when any three adjacent elements are bracketed inside a sequence of five operands.

Similarly, an -ary operation is -ary associative if bracketing any adjacent elements in a sequence of operands do not change the result.^[1]

Notes and References

1. .