On Composite Abstract Homogeneous Polynomials
نویسندگان
چکیده
منابع مشابه
Two Results on Homogeneous Hessian Nilpotent Polynomials
Let z = (z1, · · · , zn) and ∆ = ∑n i=1 ∂ 2 ∂z i the Laplace operator. A formal power series P (z) is said to be Hessian Nilpotent(HN) if its Hessian matrix HesP (z) = ( ∂ 2 P ∂zi∂zj ) is nilpotent. In recent developments in [BE1], [M] and [Z], the Jacobian conjecture has been reduced to the following so-called vanishing conjecture(VC) of HN polynomials: for any homogeneous HN polynomial P (z) ...
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where each <p,(z) is a polynomial of degree greater than unity, prime or composite, we shall say that (2) is a decomposition of F(z). The first result of the present paper is that any two decompositions of a given polynomial into prime polynomials contain the same number of polynomials; the degrees of the polynomials in one decomposition are the same as those in the other, except, perhaps, for ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1969
ISSN: 0002-9939
DOI: 10.2307/2036917