I'm looking for references, if there is any, for this problem:
Characterize all elements $a \in M_n(\mathbb{Z})$ for which we have $\mathbb{Q}[a] \cap M_n(\mathbb{Z})=\mathbb{Z}[a].$
Here, by $C[a]$ I mean the ring of polynomials in $a$ with coefficients in a ring $C.$
Thank you