A Combinatorial Property of Ideals in Free Profinite Monoids
نویسنده
چکیده
The second statement of Corollary 3 was first proved by Almeida and Volkov using techniques coming from symbolic dynamics [2]. Our next result generalizes a result of Rhodes and the author showing that all elements of finite order in F̂V(A) are group elements, which played a key role in proving that such elements are in fact idempotent [7]. Let N̂ denote the profinite completion of the monoid of natural numbers; it is in fact a profinite semring. We use ω for the non-zero idempotent of N̂.
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