Some combinatorial questions about polynomial mappings
type: Item
instance of: scholarly article
title: Some combinatorial questions about polynomial mappings
zbMATH Open document ID: 0899.13009
DOI: 10.1016/S0022-4049(96)00043-6
author: Vladimir Shpilrain
author: Arno van den Essen
published in: Journal of Pure and Applied Algebra
publication date: 1998-11-10T00:00:00Z
review text: Coordinate polynomials are elements of \(P_n= K[x_1, \dots, x_n]\), \(K\) a commutative field, which can be included in a generating set of \(P_n\) of cardinality \(n\). The authors prove that an endomorphism of \(P_2\) which fixes the set of coordinate polynomials is actually an automorphism. Assuming the Jacobian conjecture this result holds for arbitrary \(n\), too. Other results concern so-called test polynomials, for which \(\varphi (p)=p\), \(\varphi\in \text{End} P_n\), implies \(\varphi\) is an automorphism.
Mathematics Subject Classification ID: 13B25
Mathematics Subject Classification ID: 13B10
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 14H37
zbMATH DE Number: 1025719
zbMATH Keywords: coordinate polynomials
zbMATH Keywords: endomorphism
zbMATH Keywords: Jacobian conjecture
zbMATH Keywords: test polynomial
reviewed by: Gerhard Kowol
MaRDI profile type: Publication
cites work: The Jacobian conjecture: Reduction of degree and formal expansion of the inverse
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cites work: Recognizing automorphisms of the free groups
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description: scientific article; zbMATH DE number 1025719