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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.07617 |
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Table of Contents:
- Let $<X>$ be the free monoid on a generating set $X$, and suppose one adjoins to $<X>$ universal 2-sided inverses to a finite set $S$ of its elements. We note an elementary algorithm which yields a normal form for elements of the resulting monoid $M$. We then show that if $S$ is allowed to be infinite, a similar normal form exists, though it cannot necessarily be computed algorithmically. We raise a couple of questions. We note work by others on the related topic of monoids presented by finite families of relations of the form $w = 1$.