Some remarks to the Jacobian conjecture

• Autorzy: Lara-Dziembek S. , Biernat G. , Pawlak E.

Identyfikatory

DOI

10.17512/jamcm.2017.1.08

• Języki publikacji: EN

Abstrakty

EN

This work is related to the Jacobian Conjecture. It contains the formulas concerning algebraic dependence of the polynomial mappings having two zeros at infinity and the constant Jacobian. These relations mean that such mappings are non-invertible. They reduce the Jacobian Conjecture only to the case of mappings having one zero at infinity. This case is already solved by Abhyankar. The formulas presented in the paper were illustrated by the large example.

Słowa kluczowe

EN

Jacobian; zero at infinity; Jacobian Conjecture

PL

Jacobian; zero w nieskończoności; hipoteza Jakobianowa; odwzorowanie wielomianu

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2017
• Tom: Vol. 16, nr 1
• Strony: 87--96
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Lara-Dziembek S.

• Institute of Mathematics, Czestochowa University of Technology Częstochowa, Poland

autor

Biernat G.

• Institute of Mathematics, Czestochowa University of Technology Częstochowa, Poland

autor

Pawlak E.

• Institute of Mathematics, Czestochowa University of Technology Częstochowa, Poland

Bibliografia

• [1] Abhyankar S.S., Expansion techniques in algebraic geometry, Tata Inst. Fundamental Research, Bombay 1977.
• [2] Charzyński Z., Chądzyński J., Skibinski P., A Contribution to Keller’s Jacobian Conjecture, Lecture Notes In Math. 1165, Springer-Verlag, Berlin, Heidelberg, New York 1985, 36-51.
• [3] Wright D., On the Jacobian conjecture, Illinois J. Math. 1981, 25, 3, 423-440.
• [4] Van den Essen A., Polynomial automorphisms and the Jacobian conjecture, Progress in Matematics 190, Birkhäuser Verlag, Basel 2000.
• [5] Bass H., Connell E.H., Wright D., The Jacobian conjecture: reduction of degree and formal expansion of the inverse, American Mathematical Society. Bulletin. New Series 1982, 7(2), 287-330.
• [6] Fulghesu D., An Introduction to the Jacobian Conjecture, Minnesota State University Moorhead, October 12, 2010.
• [7] Drużkowski L.M., The Jacobian Conjecture, Uniwersytet Jagielloński, Kraków 1993.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).