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
( a b c ) d e = a ( b c d ) e = a b ( c d e ) ; {\displaystyle (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.
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