Frobenius extensions about centralizer matrix algebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914338895298560 |
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| author | Wang, Qikai Zhu, Haiyan |
| author_facet | Wang, Qikai Zhu, Haiyan |
| contents | This paper investigates the conditions under which the centralizer algebra $S_n(c,R)$ of a matrix $ c\in M_n(R)$ is a (separable) Frobenius extension of the base algebra $R$. For an algebra $R$ over an integral domain $\mathbb{k}$, we provide necessary and sufficient conditions for $S_n(c,R)/R$ to be a (separable) Frobenius extension when $c$ is in Jordan canonical form with eigenvalues in $\mathbb{k}$. We extend this analysis to arbitrary matrices over a field and derive conditions for matrix diagonalizability through Frobenius extensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17328 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Frobenius extensions about centralizer matrix algebras Wang, Qikai Zhu, Haiyan Rings and Algebras 15A27, 16S50, 16U70 This paper investigates the conditions under which the centralizer algebra $S_n(c,R)$ of a matrix $ c\in M_n(R)$ is a (separable) Frobenius extension of the base algebra $R$. For an algebra $R$ over an integral domain $\mathbb{k}$, we provide necessary and sufficient conditions for $S_n(c,R)/R$ to be a (separable) Frobenius extension when $c$ is in Jordan canonical form with eigenvalues in $\mathbb{k}$. We extend this analysis to arbitrary matrices over a field and derive conditions for matrix diagonalizability through Frobenius extensions. |
| title | Frobenius extensions about centralizer matrix algebras |
| topic | Rings and Algebras 15A27, 16S50, 16U70 |
| url | https://arxiv.org/abs/2602.17328 |