Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/de-gruyter/rewriting-systems-and-embedding-of-monoids-in-groups-zUODO0nNzS
- Publisher
- de Gruyter
- Copyright
- © Heldermann Verlag
- ISSN
- 1867-1144
- eISSN
- 1869-6104
- DOI
- 10.1515/GCC.2009.131
- Publisher site
- See Article on Publisher Site
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 ℜ that satisfies the condition that each rule in ℜ with positive left-hand side has a positive right-hand side, then the monoid presented by the subset of positive rules from ℜ 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 that Artin monoids embed in their groups.
Journal
Groups - Complexity - Cryptology – de Gruyter
Published: Apr 1, 2009