Abstract:It is well-known that if $n\times n$ integral matrices $A$ and $B$ of a number field $K$ are similar over all completions of the ring of integers of $K$, then $A$ and $B$ are similar over the ring of integers of a finite extension of $K$. We prove that there is no uniform bound of the degree of extension of $K$ valid for all $n\times n$ matrices. On the other hand, we provide a upper bound of the degree of extension of $K$ for a given separable characteristic polynomial.
From: Ziyang Zhu [view email]
[v1]
Fri, 19 Jun 2026 17:33:40 UTC (10 KB)
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