Test Polynomials

In this paper we show that a generic polynomial p 2 C [x 1 ; :::; x n ] of degree greater than n is a strong test polynomial for monomorphisms of C [x 1 ; :::; x n ]: We give also examples of strong test polynomial in the class of all endomorphisms of C [x 1 ; :::; x n ]: In particular we show that a generic polynomial p 2 C [x; y] of degree greater than 3 is a strong test polynomial in the class of all endomorphisms of C [x; y]: 1 Introduction Let OE : C [x 1 ; :::; x n ] ! C [x 1 ; :::; x n ] be an endomorphism of a polynomial ring. Following [1] we can ask, whether an endomorphism OE can be distinguished from non-automorphisms by means of their value on just a single polynomial. A polynomial which has this property we will call a test polynomial. MSC Classification: 14 E 10, 14 E 22, 14 E 40. Key words: polynomialautomorphisms, test polynomials, polynomialendomorphisms. *) This paper is partially supported by the grant of KBN. More formally: we look for polynomials p with the fo..