New classes of test polynomials of polynomial algebras

A polynomial p in a polynomial algebra over a field is called a test polyno mial if any endomorphism of the polynomial algebra that fixes p is an autom orphism. some classes of new test polynomials recognizing nonlinear automor phisms of polynomial algebras are given. In the odd prime characteristic ca se, test polynomials recognizing non-semisimple automorphisms are also cons tructed.