TEST POLYNOMIALS FOR AUTOMORPHISMS OF POLYNOMIAL AND FREE ASSOCIATIVEALGEBRAS

In this paper we consider test polynomials in the polynomial algebra a nd the free associative algebra. A test polynomial is defined by the f ollowing property: every endomorphism which fixes the polynomial is an automorphism. We construct families of test polynomials for the polyn omial algebra and the free associative algebra and show how different techniques may be used in the investigation of test polynomials. We al so introduce the notion of a test vector space and determine all test vector spaces of the free associative algebra. (C) 1998 Academic Press .