A Combinatorial Property of Ideals in Free Profinite Monoids
Group Theory
2008-11-11 v1 Combinatorics
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.
Cite
@article{arxiv.0811.1274,
title = {A Combinatorial Property of Ideals in Free Profinite Monoids},
author = {Benjamin Steinberg},
journal= {arXiv preprint arXiv:0811.1274},
year = {2008}
}