Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.23982 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911543478714368 |
|---|---|
| author | Facchini, Alberto Finocchiaro, Carmelo Antonio |
| author_facet | Facchini, Alberto Finocchiaro, Carmelo Antonio |
| contents | Let $S$ be a right group. Then there exist two congruences $\sim$ and $\equiv$ on $S$ such that $S$ is the product of its quotient semigroups $S/{\sim}$ and $S/{\equiv}$, where $S/{\sim}$ is a group and $S/{\equiv}$ is a right zero semigroup. If $E$ is the set of all idempotents of $S$ and we fix an element $e_0\in E$, then the pointed right group $(S,e_0)$ is the coproduct of its pointed subsemigroups $(Se_0,e_0)$ and $(E,e_0)$ in the category of pointed right groups. In general, there is a pretorsion theory in the category of right groups in which the torsion objects are right zero semigroups and the torsion-free objects are groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23982 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A pretorsion theory for right groups Facchini, Alberto Finocchiaro, Carmelo Antonio Category Theory 18B40, 18E40, 20M07 Let $S$ be a right group. Then there exist two congruences $\sim$ and $\equiv$ on $S$ such that $S$ is the product of its quotient semigroups $S/{\sim}$ and $S/{\equiv}$, where $S/{\sim}$ is a group and $S/{\equiv}$ is a right zero semigroup. If $E$ is the set of all idempotents of $S$ and we fix an element $e_0\in E$, then the pointed right group $(S,e_0)$ is the coproduct of its pointed subsemigroups $(Se_0,e_0)$ and $(E,e_0)$ in the category of pointed right groups. In general, there is a pretorsion theory in the category of right groups in which the torsion objects are right zero semigroups and the torsion-free objects are groups. |
| title | A pretorsion theory for right groups |
| topic | Category Theory 18B40, 18E40, 20M07 |
| url | https://arxiv.org/abs/2603.23982 |