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License Agreement on scientific materials use.
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ON THE SOLUTION OF JACOBIAN PROBLEM
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Vadim Nikolaevich Romanov
Saint Petersburg
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Submitted:
October 12, 2016
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Abstract.
The article gives a solution of Jacobian problem for the ring of polynomials over the field of complex numbers depending on two parameters. Examples show relationship between mutual one-oneness of mapping determined by polynomials and Jacobian finiteness. The paper identifies the conditions of the validity of Jacobian criterion. The statement proving is carried out with the induction method on the basis of the degree of the polynomial. The author suggests a way to generalize the statement in case of polynomials in several variables.
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Key words and phrases:
алгебра
поле комплексных чисел
проблема якобиана
полином
автоморфизм кольца многочленов
функциональный определитель
гессиан
algebra
field of complex numbers
Jacobian problem
polynomial
polynomial ring automorphism
functional determinant
Hessian
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References:
- Верден ван дер Б. Л. Алгебра. М.: Наука, 1976. 648 с.
- Гурвиц А., Курант Р. Теория функций. М.: Наука, 1968. 618 с.
- Пуанкаре А. Избранные труды. М.: Наука, 1972. Т. 2. Топология. 999 с.
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