Test polynomials
type: Item
instance of: scholarly article
title: Test polynomials
zbMATH Open document ID: 0972.14004
DOI: 10.1016/S0022-4049(98)00135-2
author: Z. Jelonek
published in: Journal of Pure and Applied Algebra
publication date: 2001-02-20T00:00:00Z
review text: A polynomial \(p\in\mathbb C[x_1,\dots ,x_n]\) is called a test polynomial (resp. a strong test polynomial) if for any automorphism \(\psi\) and for any endomorphism \(\phi\) of \(\mathbb C[x_1,\dots ,x_n]\) the equality \(\phi(p) =\psi(p)\) implies that \(\phi\) is an automorphism (resp. \(\phi=\psi\)). The main results of the paper are: (1) The generic polynomial \(p\) of degree \(>n\) is a strong test polynomial in the class of all monomorphisms of \(\mathbb C[x_1,\dots ,x_n]\), (2) For every \(D>0\) there is a strong test polynomial \(p\) of degree \(>D\), (3) For \(n=2\) a generic polynomial of degree \(>3\) is a strong test polynomial and a generic polynomial of degree \(\leq 3\) is not a test polynomial.
Mathematics Subject Classification ID: 14E05
Mathematics Subject Classification ID: 14E22
Mathematics Subject Classification ID: 14R15
Mathematics Subject Classification ID: 14B25
zbMATH DE Number: 1437016
zbMATH Keywords: test polynomial
zbMATH Keywords: automorphism
zbMATH Keywords: polynomial ring
reviewed by: Tadeusz Krasiński
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1437016