A Combinatorial Property of Ideals in Free Profinite Monoids

Details A Combinatorial Property of Ideals in Free Profinite Monoids A Combinatorial Property of Ideals in Free Profinite Monoids

2008-11-08

arxiv.org/abs/0811.1274v1

Mathematics

Group Theory

Scientific paper

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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