Matrix Identities Connected with the Jacobian Conjecture
نویسنده
چکیده
Let f ∈ C[x, y] be a polynomial in two variables with complex coefficients. f is said to be a component of an automorphism if there exists a polynomial g ∈ C[x, y] such that F := (f, g) : C −→ C is a polynomial automorphism of C (i.e. there exists F and it is also polynomial). In turn, f is said to be a Keller’s component if there exists g ∈ C[x, y] such that the jacobian Jac(f, g) of the mapping (f, g) : C −→ C is a non-zero constant. Then g is called associated with f and the pair (f, g) a Keller’s mapping. It is well-known that the famous (and unsolved so far) jacobian conjecture can be formulated in the following way: (1) If f is a Keller’s component, then f is a component of an automorphism. It is easy to show that it sufficies to prove (1) for f ∈ C[x, y] satisfying the following three conditions which will be called in the sequel the main assumptions: 1. f is of the form
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تاریخ انتشار 1995