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Let $\mathcal{R}$ be a valuation ring, and consider an $\mathcal{R}$-linear endomorphism $L:\mathcal{R}^{n}\rightarrow \mathcal{R}^{n}$. Is there any criterion for telligtelling when $L$ can be diagonalized? I would be specially interested in the case where $L$ is an automorphism and $\mathcal{R}$ is the valuation ring associated to a complete non-archimedean field.

Let $\mathcal{R}$ be a valuation ring, and consider an $\mathcal{R}$-linear endomorphism $L:\mathcal{R}^{n}\rightarrow \mathcal{R}^{n}$. Is there any criterion for tellig when $L$ can be diagonalized? I would be specially interested in the case where $L$ is an automorphism and $\mathcal{R}$ is the valuation ring associated to a complete non-archimedean field.

Let $\mathcal{R}$ be a valuation ring, and consider an $\mathcal{R}$-linear endomorphism $L:\mathcal{R}^{n}\rightarrow \mathcal{R}^{n}$. Is there any criterion for telling when $L$ can be diagonalized? I would be specially interested in the case where $L$ is an automorphism and $\mathcal{R}$ is the valuation ring associated to a complete non-archimedean field.

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FPV
FPV
  • 541
  • 3
  • 15

Diagonalization over valuation rings

Let $\mathcal{R}$ be a valuation ring, and consider an $\mathcal{R}$-linear endomorphism $L:\mathcal{R}^{n}\rightarrow \mathcal{R}^{n}$. Is there any criterion for tellig when $L$ can be diagonalized? I would be specially interested in the case where $L$ is an automorphism and $\mathcal{R}$ is the valuation ring associated to a complete non-archimedean field.