Adjoining universal inverses to families of elements of free monoids
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912638156406784 |
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| author | Bergman, George M. |
| author_facet | Bergman, George M. |
| 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 $w = 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07617 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adjoining universal inverses to families of elements of free monoids Bergman, George M. Group Theory 20M05 (Primary), 03B25, 08A40 (Secondary) 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 $w = 1$. |
| title | Adjoining universal inverses to families of elements of free monoids |
| topic | Group Theory 20M05 (Primary), 03B25, 08A40 (Secondary) |
| url | https://arxiv.org/abs/2510.07617 |