The Inverse Monoid of Partial Inner Automorphisms of a Semigroup
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
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| _version_ | 1866911637489844224 |
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| author | Araújo, João Bentz, Wolfram Kinyon, Michael Malheiro, Janusz Konieczny António Mercier, Valentin |
| author_facet | Araújo, João Bentz, Wolfram Kinyon, Michael Malheiro, Janusz Konieczny António Mercier, Valentin |
| contents | We introduce the inverse monoid of inner partial automorphisms of a semigroup -- a tool that associates to every semigroup an inverse semigroup. When the semigroup is a group, this inverse semigroup is isomorphic to the group of inner automorphisms with a zero adjoined. We then describe this structure for completely simple semigroups, the full transformation monoid, and the endomorphism monoid of a finite $G$-set when $G$ is a finite abelian group. The paper ends with some open problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00041 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Inverse Monoid of Partial Inner Automorphisms of a Semigroup Araújo, João Bentz, Wolfram Kinyon, Michael Malheiro, Janusz Konieczny António Mercier, Valentin Group Theory 20M10, 20M15, 20M20 We introduce the inverse monoid of inner partial automorphisms of a semigroup -- a tool that associates to every semigroup an inverse semigroup. When the semigroup is a group, this inverse semigroup is isomorphic to the group of inner automorphisms with a zero adjoined. We then describe this structure for completely simple semigroups, the full transformation monoid, and the endomorphism monoid of a finite $G$-set when $G$ is a finite abelian group. The paper ends with some open problems. |
| title | The Inverse Monoid of Partial Inner Automorphisms of a Semigroup |
| topic | Group Theory 20M10, 20M15, 20M20 |
| url | https://arxiv.org/abs/2605.00041 |