Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2603.26315 |
| Tags: |
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Inhaltsangabe:
- This article determines the structure of the group ring $\mathbb{Z}_nG$, where $G$ is a finite group and $\mathbb{Z}_n$ is the ring of integers modulo $n$, such that $n$ is relatively prime to the order of $G$. The decomposition of $\mathbb{Z}_nG$ is given as a direct sum of matrix rings over Galois rings, thereby extending the structural theory of group rings beyond the classical field setting. We also provide a method to compute a generating set of the unit group $\mathcal{U}(\mathbb{Z}_nG)$, in terms of elementary matrices, using Shoda pair theory. The results are illustrated with examples.