Similarity of Matrices over Dedekind Rings

Ziyang Zhu

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arXiv · 2405.08501

Similarity of Matrices over Dedekind Rings

Ziyang Zhu

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Abstract

We extend Latimer and MacDuffee's theorem to a general commutative domain and apply this result to study similarity of matrices over integral rings of number fields. We also conjecture similarity over discrete valuation rings can be descent by a finite covering and verify this conjecture for $2\times2$ matrices and separable characteristic polynomials.

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Ziyang Zhu. 2024-05-14. Similarity of Matrices over Dedekind Rings. https://arxiv.org/abs/2405.08501

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