منابع مشابه
Proof of Two Dimensional Jacobian Conjecture
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...
متن کاملProof of Two Dimensional Jacobian Conjecture 1
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.
متن کاملDetailed Proof of Two Dimensional Jacobian Conjecture
We give a full proof of the two dimensional Jacobian conjecture.
متن کاملThe Divergence-free Jacobian Conjecture in Dimension Two
A special case, called the divergence-free case, of the Jacobian Conjecture in dimension two is proved. This note outlines an argument for a special case of the Jacobian conjecture in dimension two: Suppose F : C → C is a polynomial so that F (0) = 0, F ′(0) = I, det(F ′(z)) = 1, z ∈ C. (1) where I is the identity transformation on C. Write F (x, y) = ( r(x, y) + x s(x, y) + y ) , (x, y) ∈ C wh...
متن کاملOn 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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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1985
ISSN: 0022-4049
DOI: 10.1016/0022-4049(85)90099-4