Products of idempotents in a quaternion ring
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915789993410560 |
|---|---|
| author | Dolžan, David |
| author_facet | Dolžan, David |
| contents | Let $R$ be a finite commutative local principal ring, and let $H(R)$ denote the corresponding quaternion ring. We show that an element of $H(R)$ is a product of idempotents if and only if it can be expressed as a product of two idempotents. Moreover, we obtain an explicit formula for the number of elements of $H(R)$ admitting such a factorization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20183 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Products of idempotents in a quaternion ring Dolžan, David Rings and Algebras 16P10, 16U40, 16U99, 11R52 Let $R$ be a finite commutative local principal ring, and let $H(R)$ denote the corresponding quaternion ring. We show that an element of $H(R)$ is a product of idempotents if and only if it can be expressed as a product of two idempotents. Moreover, we obtain an explicit formula for the number of elements of $H(R)$ admitting such a factorization. |
| title | Products of idempotents in a quaternion ring |
| topic | Rings and Algebras 16P10, 16U40, 16U99, 11R52 |
| url | https://arxiv.org/abs/2512.20183 |