Department of Mathematics
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A function \(f:A^n\rightarrow A\) is quasitrivial if \(f(a_1,\ldots,a_n)\in\{a_1,\ldots,a_n\}\). \((A,f)\) is an \(n\)-semigroup if it satisfies the generalized associative laws; e.g., for \(n = 3\), \(f(f(x,y,z),u,v) = f(x,f(y,z,u),z) = f(x,y,f(z,u,v))\). For the semigroup case (\(n = 2)\), the characterization is well known. I will present Ackerman's characterization for \(n \ge 3\).