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Abstract
We explore some combinatorial properties of singular Artin monoids and invoke them to prove that a positive singular Artin monoid of arbitrary Coxeter type necessarily injects into the corresponding singular Artin monoid. This is an extension of L. Pari' result that positive Artin monoids embed in the correpsonding Artin groups: Adjoining inverses of the generators does not produce any new identities between words that do not involve those inverses.
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ACKNOWLEDGMENT
The author would like thank Dr. David Easdown for his encouragement and many useful discussions. The work in this article was undertaken while the author was supported by an Australian Postgraduate Award.
Notes
1The reader is referred to Fenn et al. (Citation1996, Proposition 5.1) for a (geometric) proof of this result, when M = A n , without calling forth the embedding of (B n+1 =) G A n into a group.
Communicated by V. Gould.