%0 Journal Article
%T Rewriting Systems and Embedding of monoids in groups
%A Fabienne Chouraqui
%J Mathematics
%D 2008
%I arXiv
%R 10.1515/GCC.2009.131
%X 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 $\Re$ that satisfies the condition that each rule in $\Re$ with positive left-hand side has a positive right-hand side, then the monoid presented by the subset of positive rules from $\Re$ 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.
%U http://arxiv.org/abs/0804.1206v2