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n-ary associativity

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In algebra, n-ary associativity is a generalization of the associative law to n-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 n-ary operation is n-ary associative if bracketing any n adjacent elements in a sequence of n + (n − 1) operands do not change the result.[1]

References

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  1. ^ Dudek, W.A. (2001), "On some old problems in n-ary groups", Quasigroups and Related Systems, 8: 15–36, archived from the original on 2009-07-14.