Rewriting Systems and Embedding of monoids in groups
Group Theory
2011-02-01 v2
Abstract
In this paper, a connection between rewriting systems and embedding of monoids in groups is found. We show that if a group with a positive presentation has a complete rewriting system that satisfies the condition that each rule in with positive left-hand side has a positive right-hand side, then the monoid presented by the subset of positive rules from embeds in the group. As an example, we give a simple proof that right angled Artin monoids embed in the corresponding right angled Artin groups. This is a special case of the well-known result of Paris \cite{paris} that Artin monoids embed in their groups.
Keywords
Cite
@article{arxiv.0804.1206,
title = {Rewriting Systems and Embedding of monoids in groups},
author = {Fabienne Chouraqui},
journal= {arXiv preprint arXiv:0804.1206},
year = {2011}
}