n-ary associativity

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In algebra, n-ary associativity is a generalization of the associative law 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.[1]


  1. ^ Dudek, W.A. (2001), "On some old problems in n-ary groups", Quasigroups and Related Systems, 8: 15–36 .