Products of nilpotents in a quaternion ring of odd order
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918260897742848 |
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| author | Dolžan, David |
| author_facet | Dolžan, David |
| contents | Let $R$ be a finite commutative local principal ring of cardinality $q^n$, where $q = p^r$ for an odd prime $p$ and integer $r$ with $R/J(R) \simeq GF(q)$. We determine the number of elements in the quaternion ring $H(R)$ that can be expressed as a product of at least $2n-1$ nilpotent elements, and show by example that this bound is sharp. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20189 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Products of nilpotents in a quaternion ring of odd order Dolžan, David Rings and Algebras 16P10, 16H05, 16N40, 11R52 Let $R$ be a finite commutative local principal ring of cardinality $q^n$, where $q = p^r$ for an odd prime $p$ and integer $r$ with $R/J(R) \simeq GF(q)$. We determine the number of elements in the quaternion ring $H(R)$ that can be expressed as a product of at least $2n-1$ nilpotent elements, and show by example that this bound is sharp. |
| title | Products of nilpotents in a quaternion ring of odd order |
| topic | Rings and Algebras 16P10, 16H05, 16N40, 11R52 |
| url | https://arxiv.org/abs/2512.20189 |