RATIONAL IDENTITIES OF MATRICES AND A THEOREM OF BERGMAN,G.M.

In this note we present a short proof of a fundamental result of G.M. Bergman on the rational identities of generic division algebras. The m ethod of proof also allows us to force some rational identities holdin g in n x n matrices to hold in m x m matrices also for m less-than-or- equal-to n thereby extending the classical result on polynomial identi ties.