منابع مشابه
On the Jacobian Conjecture
The Jacobian Conjecture can be generalized and is established : Let S be a polynomial ring over a field of characteristic zero in finitely may variables. Let T be an unramified, finitely generated extension of S with T = k . Then T = S. Let k be an algebraically closed field, let k be an affine space of dimension n over k and let f : k −→ k be a morphism of algebraic varieties. Then f is given ...
متن کاملOn Jacobian conjecture
Any endomorphism of Cn defined by n polynomials with everywhere non-vanishing Jacobian is an automorphism. The Jacobian conjecture originated fromKeller ([5]). Let F1, . . . , Fn ∈ C[x1, . . . , xn] be a set of n polynomials in n variables with n ≥ 1 such that the Jacobian of these polynomials is a nonzero constant. The Jacobian conjecture says that the subalgebra C[F1, . . . , Fn] of C[x1, . ....
متن کاملSome Remarks on the Jacobian Conjecture and Connections with Hilbert’s Irreducibility Theorem
We have two main results. 1. Let P : Kn → Kn be a polynomial map with constant nonzero Jacobian, where K is any extension of Q. Then, P has a polynomial inverse if and only if the range of P contains a cartesian product of n universal Hilbert sets. 2. Let P : K → K be a polynomial map with constant nonzero Jacobian, where K is an algebraic number field. Then, P is invertible for “almost all” ra...
متن کاملA Note on the Jacobian Conjecture
In this paper we consider the Jacobian conjecture for a map f of complex affine spaces of dimension n. It is well-known that if f is proper then the conjecture will hold. Using topological arguments, specifically Smith theory, we show that the conjecture holds if and only if f is proper onto its image.
متن کاملOn the Jacobian Conjecture and Its Generalization
The Jacobian Conjecture can be generalized and is established : Let S be a polynomial ring over a field of characteristic zero in finitely may variables. Let T be an unramified, finitely generated extension of S with T = k. Then T = S. Let k be an algebraically closed field, let k be an affine space of dimension n over k and let f : k −→ k be a morphism of algebraic varieties. Then f is given b...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1997
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.6816