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An ideal-theoretic approach to Keller maps. (English) Zbl 1423.14342
The author proves that the ideal generated by the Keller maps is radical if \(\operatorname{char}(K)= 0\) and gives a new proof that \(V (I_F)\) is finite, where \(I_F\) is the ideal generated by Keller maps. Then he proves that the Jacobian conjecture is equivalent to that \(I_F =\langle x_1, x_2, \dots, x_n\rangle\).
Reviewer: Yan Dan (Changsha)
MSC:
14R15 Jacobian problem
14R10 Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)
13F20 Polynomial rings and ideals; rings of integer-valued polynomials
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