Finite Presentability of Brin-Higman-Thompson Monoids via Free Jónsson-Tarski Algebras

Abstract

We show that the monoids totM_{k,1} introduced by Birget and their generalizations tot nM_{k,r} which extend the Brin-Higman-Thompson groups, can be realized as the endomorphism monoids of higher-dimensional Jónsson-Tarski algebras. We also show how elements of these monoids can be thought of as "rewrite rules". We use these representations to show that the monoids are finitely presented.

24 pages,