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The implicit operation ω is the unary operation which sends each element of a finite semigroup to the unique idempotent contained in the subsemigroup it generates. Using ω there is a well-defined algebra which is known as the free aperiodic semigroup. In this article we show that for each n, the ngenerated free aperiodic semigroup is defined by a finite list of pseudoidentities and has a decidable word problem. In the language of implicit operations, this shows that the pseudovariety of finitedoi:10.1142/s0218196701000693 fatcat:26xzuzbgwbcephkztr7gsc3qiq