Free inverse monoids are not ${\protect \rm FP}_2$
We give a topological proof that a free inverse monoid on one or more generators is neither of type left-$\mathrm{FP}_2$ nor right-$\mathrm{FP}_2$. This strengthens a classical result of Schein that such monoids are not finitely presented as monoids.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2021-10-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.247/ |
| _version_ | 1797651522233827328 |
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| author | Gray, Robert D. Steinberg, Benjamin |
| author_facet | Gray, Robert D. Steinberg, Benjamin |
| author_sort | Gray, Robert D. |
| collection | DOAJ |
| description | We give a topological proof that a free inverse monoid on one or more generators is neither of type left-$\mathrm{FP}_2$ nor right-$\mathrm{FP}_2$. This strengthens a classical result of Schein that such monoids are not finitely presented as monoids. |
| first_indexed | 2024-03-11T16:15:56Z |
| format | Article |
| id | doaj.art-1d7b20fa6a46479b92395d10ba973b4a |
| institution | Directory Open Access Journal |
| issn | 1778-3569 |
| language | English |
| last_indexed | 2024-03-11T16:15:56Z |
| publishDate | 2021-10-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj.art-1d7b20fa6a46479b92395d10ba973b4a2023-10-24T14:19:20ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692021-10-0135981047105710.5802/crmath.24710.5802/crmath.247Free inverse monoids are not ${\protect \rm FP}_2$Gray, Robert D.0Steinberg, Benjamin1School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UKDepartment of Mathematics, City College of New York, Convent Avenue at 138th Street, New York, New York 10031, USAWe give a topological proof that a free inverse monoid on one or more generators is neither of type left-$\mathrm{FP}_2$ nor right-$\mathrm{FP}_2$. This strengthens a classical result of Schein that such monoids are not finitely presented as monoids.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.247/ |
| spellingShingle | Gray, Robert D. Steinberg, Benjamin Free inverse monoids are not ${\protect \rm FP}_2$ Comptes Rendus. Mathématique |
| title | Free inverse monoids are not ${\protect \rm FP}_2$ |
| title_full | Free inverse monoids are not ${\protect \rm FP}_2$ |
| title_fullStr | Free inverse monoids are not ${\protect \rm FP}_2$ |
| title_full_unstemmed | Free inverse monoids are not ${\protect \rm FP}_2$ |
| title_short | Free inverse monoids are not ${\protect \rm FP}_2$ |
| title_sort | free inverse monoids are not protect rm fp 2 |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.247/ |
| work_keys_str_mv | AT grayrobertd freeinversemonoidsarenotprotectrmfp2 AT steinbergbenjamin freeinversemonoidsarenotprotectrmfp2 |