N-ary associativity

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

(abc)de=a(bcd)e=ab(cde);

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

↑ 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.

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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.

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