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Rewriting Systems and Embedding of Monoids in Groups

โœ Scribed by Chouraqui, Fabienne

Book ID
111937532
Publisher
Walter de Gruyter GmbH & Co. KG
Year
2009
Tongue
English
Weight
138 KB
Volume
1
Category
Article
ISSN
1867-1144

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โœฆ Synopsis

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 โ„œ that satisfies the condition that each rule in โ„œ with positive left-hand side has a positive right-hand side, then the monoid presented by the subset of positive rules from โ„œ 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.

๐Ÿ“œ SIMILAR VOLUMES

Infinite Convergent String-rewriting Sys
Infinite Convergent String-rewriting Systems and Cross-sections for Finitely Presented Monoids
โœ F. OTTO; M. KATSURA; Y. KOBAYASHI ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 635 KB

A finitely presented monoid has a decidable word problem if and only if it can be presented by some left-recursive convergent string-rewriting system if and only if it has a recursive cross-section. However, regular cross-sections or even context-free cross-sections do not suffice. This is shown by