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Rewriting Systems and Embedding of Monoids in Groups

Rewriting Systems and Embedding of Monoids in Groups 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Groups - Complexity - Cryptology de Gruyter

Rewriting Systems and Embedding of Monoids in Groups

Groups - Complexity - Cryptology , Volume 1 (1) – Apr 1, 2009

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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 - Cryptologyde Gruyter

Published: Apr 1, 2009

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