Dear All,

This is related with a problem that I'm trying to solve on my PhD dissertation in econometrics, and I thought that some mathmatician can know the answer.

What is known about a possible extension, $E$ , of the ring, $ A$ , of all n-by-n matrices with entries in $\mathbb{C}$ such that any non-constant polynomial of $ A[x] $ splits in a product of linear factors in $E[x]$?

$ax = xa$ iff $a$ is in the commutator of $E$. Moreover, $ A$ is unitary.

Thanks a lot,

Federico Carlini