n-ary associativity
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{{one source |date=May 2024}}
In algebra, {{math|n}}-ary associativity is a generalization of the associative law to arity.
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 {{mvar|n}}-ary operation is {{math|n}}-ary associative if bracketing any {{math|n}} adjacent elements in a sequence of {{math|n + (n − 1)}} operands do not change the result.{{Citation |last=Dudek |first=W.A. |title=On some old problems in n-ary groups |url=http://www.quasigroups.eu/contents/contents8.php?m=trzeci |archive-url=https://web.archive.org/web/20090714003319/http://www.quasigroups.eu/contents/contents8.php?m=trzeci |url-status=dead |archive-date=2009-07-14 |journal=Quasigroups and Related Systems |year=2001 |volume=8 |pages=15–36 }}.