New classes of test polynomials of polynomial algebras

Abstract

A polynomialp in a polynomial algebra over a field is called a test polynomial if any endomorphism of the polynomial algebra that fixesp is an automorphism. some classes of new test polynomials recognizing nonlinear automorphisms of polynomial algebras are given. In the odd prime characteristic case, test polynomials recognizing non-semisimple automorphisms are also constructed.