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arXiv · 0811.1274

A Combinatorial Property of Ideals in Free Profinite Monoids

Benjamin Steinberg
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Abstract

We prove every regular element of a free profinite monoid generates a prime ideal; in particular the minimal ideal is prime. The latter result was first proved by Almeida and Volkov using techniques from symbolic dynamics; our proof is elementary.

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Benjamin Steinberg. 2008-11-08. A Combinatorial Property of Ideals in Free Profinite Monoids. https://arxiv.org/abs/0811.1274

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