On the Jacobian conjecture in two variables
نویسندگان
چکیده
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 ...
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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, . ....
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is a nonzero constant, where A = ( ∂ fi ∂ xj )i,j=1 is the n × n Jacobian matrix of f1, ..., fn. One of the major unsolved problems of mathematics [S] (see also [B, CM, V2]), viz. the Jacobian conjecture, states that the reverse of the above statement also holds, namely, if the Jacobian determinant J(f1, ..., fn) ∈ F , then f1(x1, ..., xn), ..., fn(x1, ..., xn) ∈ F[x1, ..., xn] are generators o...
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We give a full proof of the two dimensional Jacobian conjecture. We also give an algorithm to compute the inverse map of a polynomial map.
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We give a full proof of the two dimensional Jacobian conjecture.
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1988
ISSN: 0022-4049
DOI: 10.1016/0022-4049(88)90115-6