Functional identities on matrix algebras

Abstract

Complete solutions of functional identities ${\sum }_{k\in K}{F}_k({\bar{x}}_m^k)x_k={\sum }_{l\in L}{x}_l{G}_l({\bar{x}}_m^l)$ on the matrix algebra $M_n(\mathbb{F})$ are given. The nonstandard parts of these solutions turn out to follow from the Cayley-Hamilton identity.

20 pages, comments welcome, version 2- applications have been added