A characterization of Keller maps

Details A characterization of Keller maps A characterization of Keller maps

2011-09-09

arxiv.org/abs/1109.2113v2

Mathematics

Commutative Algebra

Lemma 3.5 has been corrected

Scientific paper

Let k be a field of characteristic zero. Let phi be a k-endomorphism of the polynomial algebra k[x_1,...,x_n]. It is known that phi is an automorphism if and only if it maps irreducible polynomials to irreducible polynomials. In this paper we show that phi satisfies the jacobian condition if and only if it maps irreducible polynomials to square-free polynomials. Therefore, the Jacobian Conjecture is equivalent to the following statement: every k-endomorphism of k[x_1,...,x_n], mapping irreducible polynomials to square-free polynomials, maps irreducible polynomials to irreducible polynomials.

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