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• W2016394444 abstract "Let k be a field of characteristic zero. Let φ be a k -endomorphism of the polynomial algebra k [ x 1 , … , x n ] . It is known that φ is an automorphism if and only if it maps irreducible polynomials to irreducible polynomials. In this paper we show that φ 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." @default.
• W2016394444 created "2016-06-24" @default.
• W2016394444 creator A5035499340 @default.
• W2016394444 date "2013-01-01" @default.
• W2016394444 modified "2023-09-29" @default.
• W2016394444 title "A characterization of Keller maps" @default.
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• W2016394444 doi "https://doi.org/10.1016/j.jpaa.2012.06.015" @default.
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