Keller映射的一个刻划
A characterization of Keller maps
摘要：
设k是特征为零的域。设φ是多项式代数k[x_1，…，x_n]。已知φ是自同构当且仅当它将不可约多项式映射到不可约多项式。本文证明了φ满足雅可比条件的充要条件是它将不可约多项式映射为无平方多项式。因此，雅可比猜想等价于以下陈述：k[x_1，...，x_n]，将不可约多项式映射到无平方多项式，将不可约多项式映射到不可约多项式。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
