F-Inverse Monoids as Weakly Schreier Extensions
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910785626701824 |
|---|---|
| author | Faul, Peter F. |
| author_facet | Faul, Peter F. |
| contents | It is known that an inverse monoid $M$ is E-unitary if and only if the following diagram is an extension: $E(M) \to M \to M/σ$, where $E(M)$ is the semilattice of idempotents and $M/σ$ is the minimal group quotient. F-inverse monoids are another fundamental class of inverse semigroup and all F-inverse monoids are E-unitary. Thus given that F-inverse monoids have an associated extension it is natural to ask if these extensions satisfy any special properties. Indeed we show that $M$ is F-inverse if and only if the aforementioned extension is weakly Schreier. This latter result allows us to make use of relaxed factor systems to provide a new characterization of F-inverse monoids. We end by restricting to the Clifford case and find a new characterization of these with much in common with Artin gluings of frames. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_08690 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | F-Inverse Monoids as Weakly Schreier Extensions Faul, Peter F. Rings and Algebras It is known that an inverse monoid $M$ is E-unitary if and only if the following diagram is an extension: $E(M) \to M \to M/σ$, where $E(M)$ is the semilattice of idempotents and $M/σ$ is the minimal group quotient. F-inverse monoids are another fundamental class of inverse semigroup and all F-inverse monoids are E-unitary. Thus given that F-inverse monoids have an associated extension it is natural to ask if these extensions satisfy any special properties. Indeed we show that $M$ is F-inverse if and only if the aforementioned extension is weakly Schreier. This latter result allows us to make use of relaxed factor systems to provide a new characterization of F-inverse monoids. We end by restricting to the Clifford case and find a new characterization of these with much in common with Artin gluings of frames. |
| title | F-Inverse Monoids as Weakly Schreier Extensions |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2501.08690 |