Abstract
Let X be a finite alphabet and Q be the set of all primitive words over X. In 1978, Chu and Town proved that if a 2 = c k x where k ≥ 2, x is a prefix word of c and a, c ∈ Q, then a = c. In this paper, we improve it into that if a m = c k x where m, k ≥ 2, x is a prefix word of c and a, c ∈ Q, then a = c. On the other hand, we give some disjunctive languages and a regular language which are related to primitive words. Languages D 1 = Da ∪ X* wb and D 2 = aD ∪ bw X* are all disjunctive languages for an arbitrary disjunctive language D, a, b ∈ X, a ≠ b and w ∈ X*, which were proved by Reis and Shyr in 1978. But there are some flaws in their proof. Also in the paper, we provide the other proof for them.
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