English

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.

Keywords

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}
}
R2 v1 2026-06-21T11:39:32.442Z